Name: ___________________________
Group Members:
___________________________
___________________________
___________________________
Projectile Motion
Purpose and Objectives
Projectile motion is the motion of an object in a plane (two dimensions) under the influence only of
gravity (free fall, air resistance neglected). The kinematic equations of motion describe the
components of such motion and may be used to analyze projectile motion. In most textbook cases,
the initial velocity of a projectile (speed and angle of projection) is given and other quantities
calculated. However, in this experiment, the unknown initial velocity will be determined from
experimental measurements. This will be done from range- fall distance measurements. The
dependence of the projectile range on the angle of projection will also be investigated so as to obtain
an experimental indication of the angle of projection that gives the maximum range.
These procedures will greatly assist in understanding some of the most basic physical principles.
After performing the experiment and analyzing the data, you should be able to do the following:
1. Describe the components of motion and how they are used in determining the velocity of a
projectile with range- fall measurements.
2. Tell how the range of a projectile varies with the angle of projection.
Equipment
Ballistic Pendulum
Masking tape
Meter-Stick
Plain paper
Protractor
Procedure
Part A.
1. With the pendulum removed or secured so as not to interfere with the projectile, position
the apparatus near one edge of the laboratory table. Shoot the ball from the gun and make a
note of where it strikes the floor. Be mindful of the other students and property.
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2. Place a sheet of paper where the ball hits the floor and tape it into position. When the ball
strikes the paper, look for the indentation mark. Make certain that the gun is fired from the
same position each time.
3. Shoot the ball five times, hitting the paper, and measure the horizontal distance or range x
the ball travels for each trial. Record these measurements in Data Table 1. The height y is
measured from the bottom of the ball (as it rests on the gun) to the floor (Figure 1). Measure
this distance, and record in the data table.
4. Compute the magnitude of the initial velocity of the ball.
Figure 1
Part B.
1. With the ballistic pendulum apparatus on the floor (with pendulum removed), elevate
the front end so that it can be fired at an angle  relative to the horizontal. (Your
instructor will tell you how to do this.) Aim the projectile down an aisle or hallway, being
careful not to aim at anything or anybody.
2. Using a protractor to set the angles of projection, fire the projectile at angles of 20°, 30°,
40°, 45°, 50°, 60°, and 70° with two or three trials for each angle. The projectile should
be aimed so that it lands as close as possible to the same spot for the trials of a particular
angle. Station one or more lab partners at a safe distance near where the projectile strikes
the floor. They are to judge the average range of the two or three trials.
3. Measure the average range for each angle of projection, and record the data in Data
Table 2. (Suggestion: It is convenient to measure the distance from the gun to the
position where the ball lands and to mark this position. The range measurement then can
be made relative to this measured mark, instead of from the starting point each time.
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Also, it is convenient to shoot toward a wall at the end of the hall or aisle or to lay a
meter stick on the floor perpendicularly to the line of flight, in order to stop the ball
from rolling.
4. Plot the range versus the angle of projection, and draw a smooth curve that fits the data
best. As might be expected, the points may be scattered widely because of the rather
crude experimental procedure. Even so, you should be able to obtain a good idea of the
angle for the maximum range. Determine this angle from the graph, and record it in
Data Table 3. The range will be measured from the floor position directly below the
center of the ball just as it leaves the gun to the marks on the paper on the floor. The
floor location is determined by putting the ball on the gun without loading the spring.
Data
Part A
Data Table 1
Trial
Range
1
2
3
4
5
Average
Vertical distance of fall, y : __________________________
Computed v0x : __________________________
Calculations (show work)
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Part B
Data Table 2
Angle of Projection
Average Range
20°
30°
40°
45°
50°
60°
70°
Angle of Projection for maximum Range : __________________________
Questions
Part A
1. What effect does the force of gravity have on the horizontal velocity of the projectile?
Explain.
2. What effect would air resistance have on the range of the projectile?
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Part B
3. Using experimental data, compute the magnitude of the initial velocity vo of the
projectile and compare this to the results of Part A of the procedure.
4. If, for a given initial velocity, the maximum range is at a projection angle of 45°, then
there must be equal ranges for angles above and below this. Show this explicitly.
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