Lab Instructions V0.

0 January 29, 2018

Projectile Motion

1 Objective
To experimentally study projectile motion.

2 Overview
Recall that a projectile is an object that is in free-fall, i.e., it moves while being subjected to
just the Earth’s gravity. When a projectile remains close to the surface of the earth and it’s
trajectory spans a distance much less than the earth’s circumference, its horizontal and ver-
tical motion get decoupled. It’s horizontal motion (say, x-direction) proceeds with constant
velocity, while it’s vertical motion (say, y-direction) proceeds as motion with constant ac-
celeration ~a = (g, pointing vertically down), where g = 9.8m/s2 . The projectile’s trajectory,
x vs.y curve, can then be readily derived from it’s x vs.t and y vs.t equations, by eliminating
t. In this experiment, you will have a shooter that can launch a projectile at one of three
possible, but unknown, speeds, and a continuously adjustable angle, which you can read-off
from the built-in protractor.

The main idea of this experiment is to launch a projectile, first, to determine its unknown
speed, by measuring the (x, y) coordinates at which the projectile lands, given it’s angle
of launch θ. Next, choose a different target, and predict the angle of launch θ that would
land the projectile at the chosen target. Finally, experimentally, verify your prediction by
checking if the projectile indeed hits the target.

3 Apparatus
1. Safety goggles
2. Projectile launcher (PL)
3. Ball, push rod and clamp(s).
4. Level and plumb line.
5. Carbon paper and white paper sheet.

For use by the physics department, Ohlone College, Fremont, CA.

Lab Instructions V0.0 January 29, 2018

6. Masking tape.
7. A long meter stick (2 m preferred) and possibly a piece of string or thin rope.

4 Precaution
• WEAR SAFETY GOGGLES.
• DO NOT LOOK INTO THE BARREL WHILE LAUNCHING.
• DO NOT POINT BARREL AT ANY PERSON.

5 Overall experimental set up

Figure 1: Experimental Setup

1. Position the PL at one end of the table, so its points along the table. Clamp it firmly,
so it does not move, even when you pull the trigger string.
2. The PL has three possible ranges: short, medium and long. As you push the ball into
the barrel with the push-rod, you will feel it click. Pick short or medium range, not
long range. Stick with the choice for the entire lab.
3. Make sure that a plumb line is attached to the PL, and you can read-off θ, the launching
angle above the horizontal. Use a level to position the PL horizontally, and read-off
the corresponding θ. if θ is not 0◦ , note the offset and factor that in for subsequent
launches.

For use by the physics department, Ohlone College, Fremont, CA.

Lab Instructions V0.0 January 29, 2018

Figure 2: Coordinate System and Trajectory

4. Choose your coordinate system: axis and origin. One choice for the origin is on the
table, vertically below the cross-hair on the PL. The cross-hair marks the exact position
of the launch, i.e., when the spring inside the PL disengages with the ball, and the
ball’s projectile motion begins.

5. Carefully measure the initial vertical position y0 and horizontal position x0 of the
cross-hair. Mark the x-coordinate with a piece of masking tape and pencil mark. This
way you can conveniently measure distances relative to x0 ,. Record (x0 , y0 ) with the
experimental data.

6. First experiment with launching, and determine the general area in which the ball
lands, for say, θ = 0◦ and θ = 45◦ .

7. Make sure that you are able to launch gently enough, so that the PL does not move.

8. Then, take a sheet of carbon paper, carbon-side up and place a white sheet of paper
on top of it. Tape them together onto the table, so that the projectile’s impact will
leave an imprint on the paper.

6 Part 1: Determine the initial launch speed v0 for a

set of launch angles.
6.1 Experimental data and calculations
1. Follow the steps below, to determine the launch speed for N = 3 different launch angles
θ = {15◦ , 45◦ , 75◦ }

2. For each launch angle θi , i = 1, ..., N , launch the projectile for M = 3 to 5 times. For
each shot, record the (xj , yj ), j = 1, ..., M coordinates of the impact point.

3. Compute the average coordinates, (< xi >, < yi >), for each θi .

For use by the physics department, Ohlone College, Fremont, CA.

Lab Instructions V0.0 January 29, 2018

4. Recall that the equation for the trajectory of the projectile is given by:
1 (x − x0 )2
y = y0 + tan θi (x − x0 ) − g 2 (1)
2 v0i cos2 θi

Derive the above equation in a separate section in your lab report.

5. Using x0 , y0 , θi , x =< xi > and y =< yi >, calculate the initial launch speed, v0i ,
from the equation of the trajectory above. Thus, you will have a single launch speed
for each θi .

Table 1: Data for Part 1

x0 =?, y0 =?, θi xj yj < xi > < yi > v0i

θ1 =? M data points M data points single value single value single value

θ2 =? M data points M data points single value single value single value

... ... ... ... ... ...

θN =? M data points M data points single value single value single value

6.2 Analysis and discussion

1. Does the launch speed depend significantly upon the launching angle? Is it reasonable?
2. Show that for y = y0 , maximum range is achieved at θ = 45◦ . Approximately, for what
angle do you achieve maximum range? Do you expect it to be different from 45◦ ? If
so, why?

7 Part 2: Predict the launch angle required to hit a

chosen target
7.1 Experimental data and calculations
1. Choose a target that is different from Part 1. For example, you can choose a small cup
or bowl or trace a small circle on a sheet of paper.
2. Position the target on the floor or raised on top of a stack of books.The idea is to
choose yT , the y− coordinate of the target to be different from the y coordinate of the
carbon-paper in Part 1. You can even choose the target to be a circle drawn on the
white board.

For use by the physics department, Ohlone College, Fremont, CA.

Lab Instructions V0.0 January 29, 2018

3. You might have to redefine your axis and origin. Carefully measure the coordinates
(xT , yT ) of the target, and if needed, y0 and x0 again.

4. FIRST CALCULATE (See next step). Shoot only AFTER you calculate, and only at
the predicted angle.

5. Predict the correct launch angle: Solve the equation of the trajectory for the unknown
θ. Hint: try to re-write the equation in terms of a single trigonometric function, instead
of two trigonometric functions.

6. Orient the PL to launch at the predicted angle and shoot!

7. Show the instructor your calculation of the predicted angle and demo the shot.

Table 2: Data for Part 2

x0 y0 xT yT θpred Did θpred work?

8 Conclusion
Briefly summarize your findings.

For use by the physics department, Ohlone College, Fremont, CA.