BER105 Engineering Principle

Numerical
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Engineering principles

Numerical
Contents
Worksheet Five – Two-Dimensional Kinematics............................................................................4
Solution 25...................................................................................................................................4
Solution 26a.................................................................................................................................4
Solution 26b.................................................................................................................................5
Solution 26c.................................................................................................................................5
Solution 27a.................................................................................................................................5
Solution 27b.................................................................................................................................5
Solution 27c.................................................................................................................................5
Solution 28a.................................................................................................................................5
Solution 28b.................................................................................................................................6
Solution 29a.................................................................................................................................6
Solution 29b.................................................................................................................................6
Solution 30a.................................................................................................................................6
Solution 30b.................................................................................................................................7
Solution 30c.................................................................................................................................7
Solution 31a.................................................................................................................................7
Solution 32...................................................................................................................................7
Solution 33a.................................................................................................................................8
Solution 33b.................................................................................................................................8
Solution 33c.................................................................................................................................8
Solution 34a.................................................................................................................................9
Solution 34b.................................................................................................................................9
Solution 34c.................................................................................................................................9
Solution 35a...............................................................................................................................10
Solution 36.................................................................................................................................10
Solution 37.................................................................................................................................10
Solution 38a...............................................................................................................................11
Solution 38b...............................................................................................................................12
Solution 38c...............................................................................................................................12
Solution 39a...............................................................................................................................12
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Numerical
Solution 39b...............................................................................................................................12
Solution 40a...............................................................................................................................12
Solution 41.................................................................................................................................13
Solution 42.................................................................................................................................14
Solution 44.................................................................................................................................15
Solution 45.................................................................................................................................16
Solution 46a...............................................................................................................................17
Solution 46b...............................................................................................................................17
Solution 47a...............................................................................................................................17
Solution 47b...............................................................................................................................18
Solution 48.................................................................................................................................18
Solution 49.................................................................................................................................19
Solution 50a...............................................................................................................................19
Solution 50b...............................................................................................................................20
Solution 50c...............................................................................................................................20
Solution 50d...............................................................................................................................20
Solution 51.................................................................................................................................20
Worksheet Six – Dynamics...........................................................................................................20
Solution 1...................................................................................................................................20
Solution 2...................................................................................................................................20
Solution 3...................................................................................................................................21
Solution 4a.................................................................................................................................21
Solution 4b.................................................................................................................................21
Solution 5...................................................................................................................................21
Solution 6...................................................................................................................................22
Solution 7...................................................................................................................................22
Solution 7b.................................................................................................................................23
Solution 8...................................................................................................................................23
Solution 9a.................................................................................................................................23
Solution 9b.................................................................................................................................23
Solution 9c.................................................................................................................................23
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Solution 10.................................................................................................................................23
Solution 11a...............................................................................................................................24
Solution 11b...............................................................................................................................24
Solution 12.................................................................................................................................25
Solution 12b...............................................................................................................................25
Solution 13.................................................................................................................................25
Solution 14a...............................................................................................................................25
Solution 14b...............................................................................................................................26
Solution 15.................................................................................................................................26
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Numerical
Worksheet Five – Two-Dimensional Kinematics
Solution 25
The position of projectile in 3 second = x = 50 * Cos30o x 3 = 130 m
As per launching point the y position is given by
y=0+voy t+0.5 g t2Putting the value
Y = 50*Sin(30o) *3 + 0.5(-9.8)*32 = 30.9
The height of the projectile = 30.9 m Ans
Solution 26a
The magnitude of the resultant velocity
v=√(v x )2+(v y )2=√(16)2+(12)2=20m/s
Solution 26b
Time taken by ball
t=2∗20∗sin 90o
9.8 =4.08s
Solution 26c
The height of the projectile is the distance covered vertically
H=202∗sin 90o2
2∗9.8 =20.5m
Solution 27a
The time for projectile can be calculated by
H=H o+vo t+1
2 g t2Putting the values
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Numerical
Then t=√−60
−0.5x 9.8=3.5 s Ans
Solution 27b
R=vm tThen
Vm = 100/3.5 = 28.6 m/s Ans
Solution 27c
The magnitude of the velocity
v=√(v x )2+(v y )2=√(28.6)2+(−34.3)2=44.64 m/s Ans
Solution 28a
Range of a projectile R=V o
2 sin 2θ
g =402∗sin64o
9.8
= 146.7 m
Solution 28b
The number of buses can accommodate
n=R
bus length =146.7
20 =7.34 buses
The last bus is cleared by
146.7−(7∗20)=6.7m
Solution 29a
Range of a projectile R=V o
2 sin 2θ
g
We can calculate angle from above equation
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