Projectile Motion

Exp. 1: Projectile Path

Equipment Needed
Item
 Projectile Launcher and plastic ball
 Movable vertical target board*
 Meter stick or measuring tape
 Graph paper
 Carbon paper
 White paper
 Sticky tape

*The target board should be as tall as the distance from the muzzle to the floor.

Purpose
The purpose of this experiment is to determine how the vertical distance a projectile
drops is related to the horizontal distance the projectile travels when the projectile is
launched horizontally.

Theory
The range is the horizontal distance, x, between the muzzle of the Launcher and the
place where the projectile hits, given by x = v0t, where v0 is the initial speed of the
projectile as it leaves the muzzle and t is the time of flight.
If the projectile is launched horizontally, the time of flight of the projectile will be
𝑥
𝑡=
𝑣0
The vertical distance, y, that the projectile falls during time, t, is given by
1 2
𝑔𝑡 𝑦=
2
where g is the acceleration due to gravity. Substituting for t in the second equation
gives

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 2 2
𝑣= 2 𝑥
2𝑣0
A plot of y versus x2 will give a straight line with a slope equal to,
𝑔
2𝑣02
Setup
1. Clamp the Projectile Launcher to a sturdy table or other horizontal surface. Mount
the Launcher near one end of the table with the Launcher aimed away from the table.
2. Adjust the angle of the Projectile Launcher to zero degrees so the ball will be
launched horizontally.
3. Fire a test shot on medium range to determine the initial position of the vertical
target board. Place the target board on the floor so that the ball hits the board near the
bottom.
4. Cover the target board with white paper. Tape carbon paper over the white paper.

Figure 1.1: Launcher setup

Procedure
1. Measure the vertical height from the floor to the muzzle and record the height in
the Data Table. Mark this height on the target.
2. Measure the horizontal distance from the muzzle of the Launcher to the target
board and record it in the Data Table.
3. Shoot the ball.
4. Move the target board about 10 to 20 cm closer to the Launcher.
5. Repeat steps 2 through 4 until the height of the ball when it strikes the target board
is about 10 to 20 cm below the height of the muzzle.
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Data Table 1.1
y0=1.25 m , x0=149.5 m

Table 1.1: x, y Data

Analysis
1. On the target board, measure the vertical distances from the muzzle level mark
down to the ball marks and record them in Table 1.1.
2. Calculate x2 for all the data points and record them in the Data Table.
3. Plot a graph of y versus x2 and draw the best-fit light through the data points.
4. Calculate the slope of the graph and record it in Table 1.2.
5. From the slope of the graph, calculate the initial speed of the ball as it leaves the
muzzle. Record the initial speed in Table 1.2.
6. Pick any x, y data point from Table 1.1. Use the vertical distance, y, to calculate the
time, t. Calculate the initial speed using this time and the horizontal distance, x.
Record the results in Table 1.2.
7. Calculate the percent difference between the two initial speeds that were found
using the different methods. Record the percent difference in Table 1.2. (To calculate
the percent difference, let A be one of the initial speed values and let B be the other
initial speed value).

𝐴−𝐵
× 100
𝐴+𝐵
2

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Data Table 1.2
Table 1.2: Compare Methods for Initial Speed
Item Value
Slope of graph
Initial speed from slope
Time of flight
Initial speed from x , y
Percent difference

Question
1. From the graph, was the best-fit line straight?
2. What does the shape of the best-fit line on the y versus x2 graph tell you about the
relationship of y and x2?
3. If you plotted a graph of y versus x, how would the graph differ from the y versus
x2 graph?
4. What shape is the path of the projectile?

Notes

University of Boumerdes, Institute of Electrical and Electronic Engineering, EE178L (Physics I Lab) 4
Exp. 2: Projectile Range versus Angle

Equipment Needed

Item
 Projectile Launcher and plastic ball
 Plumb bob and string
 Meter stick or measuring tape
 Box to make landing area same elevation as muzzle
 Graph paper
 Carbon paper
 White paper
 Sticky tape

Purpose
The purpose of this experiment is to determine how the range of the ball depends on
the launch angle. The angle that gives the greatest range is determined for shooting on
level ground.

Theory
The range is the horizontal distance, x, between the muzzle of the Launcher and the
place where the projectile hits, given by x = (v0 cos) t, where v0 is the initial speed of
the projectile as it leaves the muzzle,  is the launch angle above horizontal, and t is
the time of flight. See the figure.

Figure 2.1: Shooting on a level surface

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For the case in which the projectile hits on a surface that is the same level as the level
of the muzzle of the Launcher, the time of flight of the projectile will be twice the
time it takes for the projectile to reach the peak of its trajectory. At the peak, the
vertical speed is zero, so:
𝑣𝑦 = 0 = 𝑣0 sin  − 𝑔𝑡𝑝𝑒𝑎𝑘

where v0 is the initial speed of the projectile. Solving for the time gives an expression
for the total time of flight as:
𝑣0 sin 
𝑡 = 2𝑡𝑝𝑒𝑎𝑘 = 2
𝑔

For the case in which the projectile is launched at an angle above horizontal from a
table onto the floor, the time of flight is found using the equation for vertical motion:
1
𝑦 = 𝑦0 + 𝑣0 sin  𝑡 − 𝑔𝑡 2
2
where y0 is the initial height of the projectile in the Launcher and y is the vertical
position of the ball when it hits the floor.

Figure 2.2: Shooting from a table

Setup
1. Clamp the Projectile Launcher to a sturdy table or other horizontal surface. Mount
the Launcher near one end of the table, but aim it toward the center of the table rather
than away from the table.
2. Adjust the angle of the Projectile Launcher to 10 degrees.
3. Put a plastic ball into the Projectile Launcher and cock it to the medium or long
range setting.
University of Boumerdes, Institute of Electrical and Electronic Engineering, EE178L (Physics I Lab) 6
• Note: In general, the experiment will not work as well on the short range setting
because the muzzle speed is more variable with the change in angle.
4. Fire one shot to locate where the ball hits. Place a box or other horizontal surface at
that location so the ball will hit the top of the box at the same level as the muzzle of
the launcher.

Figure 2.3: Shooting to a level surface

Procedure
Shooting to a Level Surface
1. Fire one shot to locate where the ball hits the top of the box. Tape a piece of white
paper on the box at this location. Tape a piece of carbon paper (carbon-side down) on
top of the white paper.
• When the ball hits the carbon paper it will leave a mark on the white paper
underneath.
2. Fire five shots.
3. Use a measuring tape to measure the horizontal distance from the muzzle to the
leading edge of the paper. (If a measuring tape is not available, use a plumb bob to
find the point on the table that is directly beneath the release point on the barrel and
measure the distance along the table from the muzzle to the leading edge of the
paper.) Record the distance in the Data Table.
4. Carefully remove the carbon paper. Measure from the leading edge of the paper to
each of the five dots and record these distances in the Data Table.
5. Increase the launch angle by 10 degrees and repeat all the steps.
6. Keep repeating for angles up to and including 80 degrees (the complementary angle
of 10 degrees).

University of Boumerdes, Institute of Electrical and Electronic Engineering, EE178L (Physics I Lab) 7
Data Table 2.1
Table 2.1: Shooting to a Level Surface

Angle 10 20 30 40 50 60 70 80
1
2
3
4
5
Average

Paper distance

Total distance

Analysis
1. Find the average of the five distances and record the results in the Data Table.
2. Add the average distance to the distance from the Launcher to the leading edge of
the white paper to get the total distance (range). Record the results in the Data Table.
3. Plot the range versus the angle and draw a smooth curve through the points.
Questions
1. From the graph, what angle gives the maximum range?
2. Is the angle for the maximum range greater or less for shooting off the table?
3. Is the maximum range further when the ball is shot off the table or on the level?

Notes

University of Boumerdes, Institute of Electrical and Electronic Engineering, EE178L (Physics I Lab) 8