Projectile Motion Lab Report: PHY 202/PHY 241 Analysis

This assignment explores projectile motion through a practical lab report. The student investigated the effects of launch angle and launch speed on the range of a projectile, using a simulation. The report includes data tables detailing range measurements for varying launch angles and speeds, as well as an analysis of the impact of air resistance. The student calculated the time of flight and range of a projectile, and created graphs to visualize the relationships between these variables. The analysis section discusses observed trends and includes relevant physics equations and references to support the findings. This assignment is designed to familiarize students with the different aspects of projectile motion.

PHY 202/PHY 241: Projectile Motion
Student’s Name
Institutional Affiliation
Date

Procedure
Part 1: Effect of launch angle on projectile range
Table 1: Data Table A
Launch angle (degrees) Range (m)
30 223
35 241.4
40 252.6
45 256.3
50 252.2
55 240.6
60 221.6
Part 2: Effect of launch speed on projectile range
Table 2: Data Table B
Launch speed (m/s) Range (m)
10 11.0
15 23.6
20 41.2
25 63.8
30 91.4
35 124.1
40 161.8

45 204.5
50 252.2
Part 3: Effect of air resistance on projectile range
Table 3: Data Table C
Launch speed (m/s) Range (m)
10 10.7
15 22.3
20 37.3
25 55.0
30 74.5
35 95.0
40 116.1
45 137.1
50 157.9
Analysis

25 30 35 40 45 50 55 60 65
200
210
220
230
240
250
260
Range versus launch angle
Launch angle (degrees)
Range (m)
Figure 1: A graph of range (m) against launch angle (degrees)
5 10 15 20 25 30 35 40 45 50 55
0
50
100
150
200
250
300
f(x) = 0.1004329004329 x² + 0.00402597402597301 x + 0.928571428571476
R² = 0.999999950182355
Range versus launch velocity
Launch speed (m/s)
Range (m)
Figure 2: A graph of range (m) against launch speed (m/s)

5 10 15 20 25 30 35 40 45 50 55
0
20
40
60
80
100
120
140
160
180
Range versus launch velocity
with air resistance
Launch speed (m/s)
Range (m)
Figure 3: A graph of range against launch speed taking into account air resistance
Questions
1)
From the graph in part A, it can be observed that initially, the projectile range increases with
the increasing launch angle up to a maximum value of 256.3 m. This is the maximum range
and it occurs at an angle of 45 degrees. Thereafter, the range increases with increasing launch
angle.
2)
From the graph in figure 2, it can be observed that the best curve that fits the data has a
parabolic equation with a coefficient of determination of R2=1. Therefore, the mathematical
relationship between range and launch velocity is parabolic with the equation,
y=0.1004 x 2+0.004 x +0.9286
3)

Comparing the data and graphs from part A and part B, it can be observed that the effect of
air resistance is to reduce the range of the projectile. For every given launch velocity, the
projectile covers less distance in the presence of air resistance compared to the situation in
which air resistance is suppressed.
4)
Consider a projectile launched at an angle θ and initial velocity u as shown in the figure
below. The initial velocity can be resolved into its vertical and horizontal component
velocities uy and ux (Mody, 2015). Where,
ux=ucos θ
uy =usinθ
The range of the projectile is simply the product of the horizontal velocity and the time taken
to hit the ground (time of flight).
R=ux ×t
R=ucos θ ×t
R=ut cos θ 1

The time, t is calculated from the time it takes the projectile to reach the maximum height
while in flight. The velocity at the maximum height can be expressed as,
v y=uy + ( −g ) tm
Where tm is the time taken to reach maximum height (half the time of flight) (Buček, 2016),
v y=uy−g tm
v y=usinθ−g tm
We recognize that the velocity of the projectile at the maximum height is zero (Tymms,
2015),
0=usinθ−g tm
g tm=usinθ
tm= usinθ
g
Therefore the time of flight, t is,
t=2 tm
t= 2usin θ
g 2
Substituting equation 2 into equation 1 we have,
R=utcosθ
R=ucos θ × 2usin θ
g
R=2 u2 sinθ cos θ
g

R=u2 (2 sin θcosθ)
g
From trigonometric identities (Cohen, 2016),
2 sin θcosθ=2 sin θ
R=u2 2 sinθ
g

References
Buček, S. (2016). Falling Objects And Projectile Motion With Regard The Air Resistance.
Edulearn16 Proceedings. doi:10.21125/edulearn.2016.0800
Cohen, I. B. (2016). Newton's concepts of force and mass, with notes on the laws of motion.
The Cambridge Companion to Newton, 61-92. doi:10.1017/cco9781139058568.004
Mody, V. (2015). High School Physics: Projectile Motion. Scotts Valley, CA: CreateSpace.
Tymms, V. (2015). Newtonian Mechanics for Undergraduates. CA: World Scientific
Publishing Company.