Prelab: Projectile Motion

Name: Date:
Group members: Instructor:

Two coins are balanced at the edge of a table. The first coin is flicked horizontally
so that it travels off the table while the second coin is gently nudged off the edge so that
they both leave the table at the same time.

1. Predict which coin will land first. Explain. (4 pts.)

2. If we increase the speed of the first coin, does the horizontal speed affect the impact
times of the coins? (3 pts.)

3. If we increase the height from which the coins are dropped, does the height affect
your answer on the first item? (3 pts.)

Prelab: Projectile Motion 1

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 EXPERIMENT
Projectile Motion

Objectives

In this experiment, the student is expected to:

• measure the launch speed of a ball using a Vernier Projectile Launcher.
• apply concepts from two-dimensional kinematics to predict the impact point of a
ball in projectile motion.
• take into account trial-to-trial variations in the speed measurement when calculating
the impact point.

Introduction

A projectile is any object that is thrown with some initial velocity and is subject to
uniform acceleration due to gravity. You may have observed one when you watched or
played any sport involving balls e.g., basketball, tennis, soccer, etc. Although the ball’s
motion might be complicated at some time, you will always notice that arching motion
as it flies unimpeded. We may model its motion by arguing the following,
1. The motion along perpendicular directions are independent.
2. The most significant contribution to produce the motion of the projectile is gravity.
The first statement urges us to use vectors in specifying our projectile’s state, i.e.
position vector and velocity vector. The second statement simplifies our model such
that the projectile will experience uniform acceleration along the vertical (downward)
direction. With these, we can write the horizontal (x-axis) and vertical (y-axis) equations
of motion separately as,
ax = 0 ay = −g (1)
vx = vx0 vy = vy0 − gt (2)
x = x0 + vx0 t y = y0 + v0y t − 21 gt2 (3)
Note the convention used in setting up the coordinate system. These equations can
be used to compute the curve of the trajectory of the projectile in space by eliminating
the time parameter in the x(t) and y(t) equations. One yields the following equation,
g
y(x) = y0 + tan(θ)(x − x0 ) − 2 2
(x − x0 )2 (4)
2v0 cos (θ)

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One can see that the trajectory looks like a parabola. In the experiment, we can
confirm this by obtaining a data set of heights (y) for every horizontal displacement
(x − x0 ). Furthermore, we can set a the y = y0 in the equation above and yield an
equation for the effective range x = R of the projectile,

v02 sin 2θ
R= (5)
g

We can confirm this relation by predicting the effective range of the projectile launched
at some angle of elevation θ and initial speed v0 .

Materials

The following materials are required for the experiment:

• Vernier Projectile Launcher

• Vernier LabQuest

• Steel Ball

• Goggles

• Metric Measuring Tape

• Carbon Paper

• White Paper

• Level

Procedure

Part 0: Initial Setup

1. Position the launcher on a flat surface and secure it so that it is immovable during
the experiment.

2. Place the level on top of the launch chamber. Use the lower knob on the back of
the unit to adjust the orientation of the launch chamber until level. Tighten the
knob to maintain this position.

3. Next, use the upper knob on the back of the launcher to set the scale to 0◦ . Move
the scale so that the notch of the launcher chamber is at 0◦ . This setting accounts
for deviation of the tabletop from horizontal.

4. Connect the Projectile Launcher to the interface by attaching one end of the digital
cable to the port labeled “Interface” on the launcher and the other end to one of
the digital ports (labeled “DIG”) in the Vernier LabQuest.

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Physics 71.1 1st Sem, A.Y. 2019–2020

5. Connect the hand pump to the Projectile Launcher. Set the release pressure by
adjusting the range knob. Turn clockwise for higher pressure and higher launch
speed and counter-clockwise for lower pressure and lower launch speed.

Note: Ask your instructor how to select an appropriate release pressure. When you
pump the hand pump, you will hear a small release sound when the pressure is reached.
Keep pumping until you hear at least three small release sounds, and then wait for five
seconds so that the pressure is stabilized. Do not adjust the release pressure for the
remainder of the activity or your prediction will be incorrect.

Part 1: Measuring Launch Speed

Warning: Wear goggles while obtaining data.

1. Insert a steel ball into the barrel. To do this, insert the ball into the launch chamber
with your index finger and guide the ball into the barrel.

2. Pump the hand pump until the pressure stabilizes. Keep pumping until you hear at
least three small release sounds and then wait for five seconds so that the pressure
is fully stabilized.

3. Collect data using the following steps.

a. Click to start data collection.
b. When you are ready to launch the ball, press and hold the Arm button, and
then press the Launch button.
c. Record the speed in the data table.

4. Repeat this process, catching the ball each time, so that you have a total of 5 launch
speed measurements. Record the values in Table W1.

5. Inspect your speed data. Calculate the average speed value Record the value in
Table W1.

Part 2: Range of a Projectile

In this part, the range of a projectile for varying launch angles will be measured.
1. Adjust the upper knob on the back of the launcher to change the launch angle.
Refer to Table W2.

2. Place the wooden platform in front of the launcher. The ball should land on the
platform to ensure that its launch point has the same height as its landing point.

3. Secure a white paper with a carbon paper on top of the platform; this will mark
the position of the ball’s landing.

4. Launch the ball using similar procedures as in Part 1 and measure the distance
between the ball’s launch and landing points. Record your data as Rexpt in Table
W2. Repeat this step for other angles indicated in Table W2

5. Do three trials per angle.

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Part 3: Height of a Projectile

In this part, the height of a projectile for varying horizontal distances will be determined.

1. Select a launch angle among those used in Part 2, then adjust the angle of the
launch chamber to this value.

2. Position the vertical wooden block at some horizontal distance in front of the
launcher. The ball should hit the block as it follows its trajectory.

3. Secure a white paper with a carbon paper on top of the platform; this will mark
the height of the ball at the set horizontal distance.

4. Launch the ball using similar procedures as in Part 1 and measure the vertical
distance between the ball’s height along its trajectory and its initial height. Record
your result as yf,expt in Table W3. Repeat this step for other horizontal distances

5. Do three trials per horizontal distance.

Part 4: Data Analysis

1. Plug in the average speed value in Equations 4 and 5 to calculate for the range
Rtheo and the height yf,theo for each angle. Record the values in Tables W2 and
W3. Compute for the percent error of the experimental values with the theoretical
values.

2. Use a spreadsheet program to graph your data in Table W2 and W3. Paste printouts
of your graphs in Figures 1 and 2.

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Physics 71.1 1st Sem, A.Y. 2019–2020

Name: Date:
Group members: Instructor:

Data Sheet

Table W1: Launch Speed

Trial Speed (m/s)

1
2
3
Average speed

Table W2: Range of a Projectile

Rexpt (m)
Angle hRexpt i (m) Rtheo (m) % error
Trial 1 Trial 2 Trial 3

Table W3: Trajectory of a Projectile

yexpt (m)
x (m) hyexpt i (m) ytheo (m) % error
Trial 1 Trial 2 Trial 3

Initial height, y0 = m

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1st Sem, A.Y. 2019–2020 Physics 71.1

sin(2θ)

Figure 1: Plot of Rexpt and Rtheo vs sin(2θ)

Figure 2: Plot of yexpt and ytheo vs. x

Questions

Answer the following questions in no more than two sentences.

1. Are your graphs consistent with the expected behavior based on Equations 4 and
5 Explain.

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Physics 71.1 1st Sem, A.Y. 2019–2020

2. What assumption(s) must be made in using Equations 4 and 5?

3. Looking at the graphs, what do you think is/are the effect(s) of air resistance on
the range and final height of a projectile?

Projectile Motion 9