BER105 Engineering Principles: Numerical Solutions and Kinematics

This assignment solution covers various topics in engineering principles, including numerical solutions for kinematics problems, measurement and mensuration, and thermodynamics. It includes detailed solutions for Assignment 3 questions, covering concepts such as projectile motion, velocity, and acceleration. The document also provides solutions to multiple worksheets focusing on measurement, kinematics, and projectile motion, offering step-by-step explanations and calculations. The worksheets cover a wide range of problems, from basic unit conversions to more complex kinematic equations and scenarios. Desklib offers many more such solved assignments and resources for students.

Numerical
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Engineering principles

Numerical
Contents
Solution of Assignment_3 question...............................................................................................11
Solution 1a.................................................................................................................................11
Solution 1b.................................................................................................................................11
Solution 1c.................................................................................................................................11
Solution 2a.................................................................................................................................12
Solution 2b.................................................................................................................................12
Solution 2c.................................................................................................................................12
Solution 2d.................................................................................................................................12
Solution 2e.................................................................................................................................13
Solution 2f.................................................................................................................................13
Solution 2g.................................................................................................................................13
Solution 3a.................................................................................................................................14
Solution 3b.................................................................................................................................14
Solution 3c.................................................................................................................................14
Solution 4a.................................................................................................................................14
Solution 4b.................................................................................................................................14
Solution 5a.................................................................................................................................15
Solution 5b.................................................................................................................................15
Solution 6a.................................................................................................................................16
Solution 6b.................................................................................................................................16
Worksheet One – Measurement and Mensuration.........................................................................16
Solution 1a.................................................................................................................................16
Solution 1b.................................................................................................................................16
Solution 2a.................................................................................................................................16
Solution 2b.................................................................................................................................17
Solution 3...................................................................................................................................17
Solution 4...................................................................................................................................17
Solution 5...................................................................................................................................17
Solution 6...................................................................................................................................17
Solution 7...................................................................................................................................17
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Solution 8...................................................................................................................................18
Solution 9a.................................................................................................................................18
Solution 9b.................................................................................................................................18
Solution 10.................................................................................................................................18
Solution 11.................................................................................................................................18
Solution 12.................................................................................................................................19
Solution 13.................................................................................................................................19
Solution 14.................................................................................................................................19
Solution 15.................................................................................................................................19
Solution 16.................................................................................................................................19
Solution 17a...............................................................................................................................19
Solution 17b...............................................................................................................................20
Solution 17c...............................................................................................................................20
Solution 18a...............................................................................................................................20
Solution 18b...............................................................................................................................20
Solution 18c...............................................................................................................................20
Solution 19a...............................................................................................................................20
Solution 19b...............................................................................................................................20
Solution 20a...............................................................................................................................20
Solution 20b...............................................................................................................................20
Solution 21.................................................................................................................................20
Solution 22.................................................................................................................................21
Solution 23.................................................................................................................................21
Solution 24.................................................................................................................................21
Solution 24a...............................................................................................................................21
Solution 24b...............................................................................................................................21
Solution 24c...............................................................................................................................21
Solution 24d...............................................................................................................................21
Solution 25.................................................................................................................................22
Solution 26.................................................................................................................................22
Solution 27.................................................................................................................................22
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Solution 28a...............................................................................................................................22
Solution 28b...............................................................................................................................22
Worksheet Two – Kinematics.......................................................................................................23
Solution 1a.................................................................................................................................23
Solution 1b.................................................................................................................................23
Solution 1c.................................................................................................................................23
Solution 2a.................................................................................................................................23
Solution 2b.................................................................................................................................23
Solution 2c.................................................................................................................................23
Solution 3a.................................................................................................................................23
Solution 3b.................................................................................................................................23
Solution 3c.................................................................................................................................23
Solution 4a.................................................................................................................................23
Solution 4b.................................................................................................................................24
Solution 4c.................................................................................................................................24
Solution 5a.................................................................................................................................24
Solution 5b.................................................................................................................................24
Solution 6...................................................................................................................................24
Solution 6...................................................................................................................................24
Solution 7...................................................................................................................................24
Solution 8...................................................................................................................................25
Solution 9...................................................................................................................................25
Solution 10.................................................................................................................................25
Solution 11a...............................................................................................................................25
Solution 11b...............................................................................................................................25
Solution 11c...............................................................................................................................25
Solution 11d...............................................................................................................................25
Solution 12.................................................................................................................................25
Solution 13.................................................................................................................................26
Solution 14a...............................................................................................................................26
Solution 14b...............................................................................................................................26
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Solution 15a...............................................................................................................................26
Solution 15b...............................................................................................................................26
Solution 16.................................................................................................................................26
Solution 17a...............................................................................................................................26
Solution 17b...............................................................................................................................26
Solution 18a...............................................................................................................................27
Solution 18b...............................................................................................................................27
Solution 19.................................................................................................................................27
Solution 20.................................................................................................................................27
Solution 21.................................................................................................................................28
Solution 22.................................................................................................................................28
Solution 23a...............................................................................................................................28
Solution 23b...............................................................................................................................28
Solution 23b...............................................................................................................................28
Solution 24a...............................................................................................................................29
Solution 24b...............................................................................................................................29
Solution 24c...............................................................................................................................29
Solution 25a...............................................................................................................................29
Solution 25b...............................................................................................................................30
Solution 25c...............................................................................................................................30
Solution 26a...............................................................................................................................30
Solution 26b...............................................................................................................................30
Solution 26c...............................................................................................................................30
Solution 26d...............................................................................................................................31
Solution 27.................................................................................................................................31
Solution 28.................................................................................................................................31
Solution 29a...............................................................................................................................31
Solution 29b...............................................................................................................................31
Solution 29c...............................................................................................................................32
Solution 30a...............................................................................................................................32
Solution 30b...............................................................................................................................32
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Solution 31a...............................................................................................................................32
Solution 31b...............................................................................................................................33
Solution 32a...............................................................................................................................33
Solution 32b...............................................................................................................................33
Solution 33a...............................................................................................................................33
Solution 33b...............................................................................................................................33
Solution 34.................................................................................................................................34
Solution 35a...............................................................................................................................34
Solution 35b...............................................................................................................................34
Solution 36a...............................................................................................................................34
Solution 36c...............................................................................................................................35
Solution 36d...............................................................................................................................35
Solution 37a...............................................................................................................................35
Solution 37b...............................................................................................................................35
Solution 37c...............................................................................................................................35
Solution 38a...............................................................................................................................35
Solution 38b...............................................................................................................................35
Solution 38c...............................................................................................................................36
Solution 39.................................................................................................................................36
Solution 40a...............................................................................................................................36
Solution 40b...............................................................................................................................37
Solution 41a...............................................................................................................................37
Solution 41b...............................................................................................................................37
Solution 41c...............................................................................................................................38
Solution 41d...............................................................................................................................38
Solution 41e...............................................................................................................................38
Solution 42a...............................................................................................................................38
Solution 42b...............................................................................................................................38
Solution 42c...............................................................................................................................39
Solution 42d...............................................................................................................................39
Solution 42e...............................................................................................................................39
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Solution 43.................................................................................................................................39
Solution 44a...............................................................................................................................39
Solution 44b...............................................................................................................................40
Solution 45a...............................................................................................................................40
Solution 45b...............................................................................................................................40
Solution 45c...............................................................................................................................40
Solution 46a...............................................................................................................................40
Solution 46b...............................................................................................................................41
Solution 46c...............................................................................................................................41
Solution 47a...............................................................................................................................41
Solution 47b...............................................................................................................................42
Solution 48.................................................................................................................................42
Solution 49.................................................................................................................................42
Solution 50a...............................................................................................................................43
Solution 50b...............................................................................................................................43
Solution 51a...............................................................................................................................43
Solution 51b...............................................................................................................................43
Solution 52a...............................................................................................................................44
Solution 52b...............................................................................................................................44
Solution 52c...............................................................................................................................44
Solution 53a...............................................................................................................................44
Solution 53b...............................................................................................................................45
Worksheet Three – Kinematics.....................................................................................................45
Solution 1a.................................................................................................................................45
Solution 1b.................................................................................................................................45
Solution 2a.................................................................................................................................45
Solution 2b.................................................................................................................................45
Solution 3...................................................................................................................................46
Solution 4...................................................................................................................................46
Solution 5...................................................................................................................................46
Solution 6...................................................................................................................................47
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Solution 7a.................................................................................................................................48
Solution 7b.................................................................................................................................49
Solution 8...................................................................................................................................49
Solution 9...................................................................................................................................50
Solution 10.................................................................................................................................51
Solution 11.................................................................................................................................52
Solution 12.................................................................................................................................52
Solution 13a...............................................................................................................................53
Solution 13b...............................................................................................................................53
Solution 14.................................................................................................................................53
Solution 15.................................................................................................................................54
Solution 16.................................................................................................................................54
Solution 17.................................................................................................................................55
Solution 18a...............................................................................................................................55
Solution 18a...............................................................................................................................56
Solution 19a...............................................................................................................................56
Solution 19b...............................................................................................................................57
Solution 20.................................................................................................................................57
Solution 21a...............................................................................................................................58
Solution 21b...............................................................................................................................59
Solution 22a...............................................................................................................................59
Solution 23.................................................................................................................................60
Worksheet Four – Kinematics.......................................................................................................61
Solution 52a...............................................................................................................................61
Solution 52b...............................................................................................................................61
Solution 52c...............................................................................................................................61
Solution 53a...............................................................................................................................61
Solution 53b...............................................................................................................................62
Solution 54a...............................................................................................................................62
Solution 54b...............................................................................................................................62
Solution 54c...............................................................................................................................62
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Solution 55.................................................................................................................................63
Solution 56.................................................................................................................................63
Solution 57.................................................................................................................................64
Solution 58.................................................................................................................................65
Solution 59a...............................................................................................................................66
Solution 59b...............................................................................................................................66
Solution 60a...............................................................................................................................67
Solution 60b...............................................................................................................................68
Solution 61a...............................................................................................................................68
Solution 61b...............................................................................................................................68
Solution 61c...............................................................................................................................68
Solution 62.................................................................................................................................69
Solution 63a...............................................................................................................................70
Solution 63b...............................................................................................................................70
Solution 64a...............................................................................................................................71
Solution 64b...............................................................................................................................71
Solution 65a...............................................................................................................................71
Solution 66.................................................................................................................................72
Solution 67.................................................................................................................................72
Solution 68a...............................................................................................................................73
Solution 68b...............................................................................................................................73
Solution 68c...............................................................................................................................73
Solution 68d...............................................................................................................................73
Solution 69a...............................................................................................................................73
Solution 69b...............................................................................................................................74
Solution 69c...............................................................................................................................74
Solution 69d...............................................................................................................................74
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Solution of Assignment_3 question
Solution 1a
As given in question,
Y = -h, a = -9.8 m/s, t =?, S = -2.0 m, u = 4.5 m/sec
We know that distance travelled is given by
S=ut+ 1
2 a t2
⟹−2=4.5 t−4.9t2
⟹ 4.9 t2−4.5 t−2=0 By solving these equations, we get,
T = 1.245 and -0.3276,
Time is non-negative, therefore, her feet in the air = 1.245 sec
Solution 1b
The highest point is calculated through v2−u2=2 aS
Putting the requied value from question (a)
s= v2−u2
2 as Putting the value in this equation,
s= 02−4.52
2(−9.8)=¿1.03316 m Ans
Solution 1c
The velocity at water level = V =u +at
⇒ v2=4.5−9.8 x 1.245 = -0.70701 m/sec
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Solution 2a
As given in question, V = 80 m/sec, g = 10 m/sec2, u = 0
We know that v2−u2=2 gh
Then, Putting the value
h= 802
2 x 10 = 6400
20 =320 m Ans
Solution 2b
Suppose the ball started from ground h = 0, Then time taken to reach the ball at the height of 320
m
S=ut+ 1
2 g t2
320=80 x t−5 t2
5 t2 −80 t+320=0
Then t = 8 sec
Time taken to reach to the ground = 8*2 = 16 sec Ans
Solution 2c
, u = 80 m/sec, g = 10 m/sec2, u = 0, t = 4 sec
The V =u +¿
Putting the value = S=80−10∗4=80−40=40 m/ sec
Solution 2d
The maximum acceleration of the ball at maximum height,
v2=u2 +2 gH
02 =802−2∗g∗320
h=6400
640 =10 m/ s2
The acceleration will be 10 m/s2 downward
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