Name ______________________________ Period ______ Catapult #_____
Physics Lab
Predicting the Range of a Projectile
Launched at an Angle
A modern day marksman does not need to know the actual path a bullet follows on
its way to a target. However, a great marksman does know the path and can make
critical aiming adjustments to hit a target at many different ranges. In this lab you
will become a great marksman. Like all great marksmen, you will master twodimensional motion by using kinematic equations to predict the path of a projectile
and hit a target. You will predict the range of a projectile, launched from a
catapult, with a certain velocity at a given angle above the horizontal.
Neglecting frictional forces, such as air resistance, an object projected from a
catapult undergoes motion that is the vector combination of uniform velocity in the
horizontal direction and uniform acceleration in the vertical direction.
Horizontal Projectile Motion
ax  0
Vertical Projectile Motion
a y  g  9.8m / s 2
vx  c
v y  gt
Horizontal Projectile Motion
at an Angle
ax  0
Vertical Projectile Motion
at an Angle
a y  g  9.8m / s 2
v x  v i cos
v y  v i sin  gt
x  v i cos t
g
y  v i sint  t12
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For a projectile launched with a speed v and at an angle θ with respect to the
positive x-axis, it can be shown that the trajectory caused by such a combination
predicts a parabolic path (Figure 1).
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Physics Lab
Predicting the Range of a Projectile
Launched at an Angle
At any point along the trajectory, the velocity vector is the vector sum of the
horizontal and the vertical vectors, that is, 𝒗 = 𝒗𝒗 + 𝒗𝒗 . Furthermore, the
components of the velocity can be written in terms of the original launch velocity:
2
2
2
By the Pythagorean Theorem, v  v x  v y
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Physics Lab
Predicting the Range of a Projectile
Launched at an Angle
Purpose
In this activity, you will study the motion of a projectile launched into the air and
allowed to fall freely, assuming negligible air friction. You will then be asked to
apply kinematic equations to accurately position a target so the projectile hits the
target.
Materials
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wooden catapult
miniature marshmallows
Physics textbook
protractor
measuring tape
masking tape
pencil
graph paper
graphing calculator
Part I: RANGE vs. ANGLE
Procedure
1. Place the catapult on a flat surface and perform a two or three practice
rounds launching marshmallows.
2. Use a textbook to prop the catapult to an angle of 10°. Use a
protractor to position the catapult arm at the correct angle.
3. Launch a marshmallow and measure the distance travelled.
4. Record data in Data Table 1.
5. Perform two more trials at the same angle.
6. Calculate the average landing position. The landing position is where
the projectile initially hits the ground, not where it eventually comes
to a rest.
7. Repeat step 2 through 5 for angles of projection from 10° through
90°in increments of 5°.
8. On the graph paper provided, make a graph of range (y) vs. angle (x).
Use a pencil and label the graph properly, neatly, and in landscape
orientation. Use as much of the paper as you can for your graph.
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Physics Lab
Predicting the Range of a Projectile
Launched at an Angle
Data Table 1
Launch Angle
(°)
Range 1
(m)
Range 2
(m)
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
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Range 3
(m)
Average Range
(m)
Physics Lab
Predicting the Range of a Projectile
Launched at an Angle
Part II: MUZZLE VELOCITY
Height
(y)
Acceleration
(g)
Flight Time
(t)
Muzzle Velocity
(vx)
Procedure
1. Place your catapult on a surface above the floor and record the height, H,
in the table provided. Use the average range for the angle of projection at
90° to calculate the time of flight for your projectile. Remember, vertical
velocity (vy) will be 0 m/s because the projectile will be launched parallel
to the horizontal plane. Record your answers in the table provided below.
As always, show all your work for all calculations.
2. Calculate the initial horizontal velocity (vx) for the projectile given its
range. With zero friction due to air resistance, horizontal velocity (vx) is
constant and the initial velocity (vi) is the muzzle velocity of the catapult.
Part III: HITTING A TARGET
Procedure
1. Use the muzzle velocity of your catapult to calculate the horizontal and
vertical components of the initial velocity when the projectile is
launched. The angle of projection will be the angle of the arm of the
catapult.
2. Find the time for the projectile to reach the maximum height above H.
3. Calculate the maximum height of the projectile.
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Physics Lab
Predicting the Range of a Projectile
Launched at an Angle
4. Calculate the time for the projectile to fall from the maximum height.
5. Calculate the range of the projectile.
6. Calculate the velocity of the projectile at the moment it hits the ground
after it is launched.
CONCLUSION QUESTIONS
Answer the following questions in complete sentences where applicable.
Part I: RANGE vs. ANGLE
1. During this activity, the range of the projectile should have a maximum value for a
given angle. According to you graph, what angle provides the maximum range?
2. Discuss why the range decreases for angles that are greater or less than the angle you
recorded for question #1.
3. Theory predicts that the maximum range of the projectile will occur at 45°. There
should be two distinct launch angles (complimentary angles whose sum is 90°) that
provide the projectile with the about the same range. Using your graph, list two pairs
of angles that yield about the same range values. Is each pair a set of complimentary
angles? Explain.
4. Suppose your projectile is launched at an angle of 58°. Use your graph to predict how
far the projectile will travel horizontally.
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Physics Lab
Predicting the Range of a Projectile
Launched at an Angle
Part II: MUZZLE VELOCITY
1. Consider the data you collected in Part II of this activity. What would a graph of
vertical distance (y) vs. time (x) look like? Stated differently, what would be the shape
of the graph?
2. If you were to plot a graph of vertical velocity (vy) versus time (t), with vertical
velocity on the y-axis and time on the x-axis, what would the plot look like? What
does this graph indicate about projectile motion?
Part III: HITTING A TARGET
A golf ball resting on the ground is struck by a golf club and given an initial velocity of
50 m/s at an angle of 30° above the horizontal. The ball heads toward a fence 12 m high
at the end of the golf course, which is 200 m away from the point at which the golf ball
was struck. Neglect any air resistance that may be acting on the golf ball.
1. Calculate the time it takes for the ball to reach the fence.
2. Will the ball hit the fence or pass over it? Justify you answer by showing you
calculations.
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