LPC Physics
Revised 02/09
Projectile Motion
Projectile Motion
Purpose:
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•
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To calculate the initial speed of a projectile by measuring its range.
To predict how far a projectile will travel when fired at different angles, and test
these predictions.
To predict what angle will produce the maximum range for a projectile fired off
the table onto the ground, and test this prediction.
Equipment:
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Ballistic Gun Apparatus
Projectiles
Table Clamps
2-meter Stick
Carbon Paper, Scratch Paper, Masking Tape
Plumb Bob
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Projectile Motion
Part I - Measuring Initial Speed
Today you are going learn about projectile motions by shooting miniature cannons all
evening. There are three things that determine how far the projectile will go once it leaves
the cannon:
1. The initial speed of the ball, written as vo ,
2. The height of the launch point above the ground, written as h,
3. The acceleration due to gravity, g.
Recall that is you drop a projectile from a height h, then the projectile will free fall, with
distance and time related by:
1
h = gt 2
2
Solving for time t, you get:
2h
t=
g
Now if you fire the ball horizontally at a speed vo instead of
dropping it, it will travel a horizontal distance R (for range) given by
R = vot,
where t is the time from the free fall equation above. So if you fire a
projectile horizontally from a height h, with a speed vo the distance it will
travel is:
R = vo
2h
.
g
Equation 1
Prelab question 1: Would increasing the height of the launch point from the ground
increase or decrease the projectile’s range? Why?
Prelab question 2: Will increasing the projectile’s initial speed increase or decrease its
range? Why?
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Projectile Motion
Prelab question 3: Which would cause the range to change more: doubling the initial
speed or doubling the height of the launch point? Show your reasoning.
We can rewrite the equation 1 in a way that lets us calculate the initial speed by
measuring the range:
g
vo = R
Equation 2
2h
We’ll use this equation with the measurements you’re about to take to determine the
speed at which your projectile leaves the launcher Follow these steps to make your
measurements:
1. Clamp the cannon to the edge of your table with the muzzle pointing away from
the table. Make sure that the cannon is completely horizontal. Also make sure
that you aren’t pointing toward any humans.
2. Your cannon is spring loaded, with three different settings. Tonight, you should
use the lowest setting. Load the projectile into the cannon by pushing it in until
you feel a click. If it clicks twice, you have gone too far! Fire the cannon by
pulling up on the release lever, and pay attention to where the projectile lands.
3. Tape down a piece of scratch paper on the floor where the projectile landed, and
tape a piece of carbon paper, carbon side down, on top of the scratch paper. Now
when you fire the cannon the projectile will strike the carbon paper and make a
mark.
4. Load and fire the cannon ten times.
5. Use a plumb bob to mark the spot on the floor directly below the cannon muzzle.
6. Pull up the carbon paper, but leave the scratch paper on the floor. Use the twometer stick to measure the distance from the launch point (that you found with the
plumb bob) to each mark on your scratch paper. Record your measurements in
the table below.
Trial Number
1
2
3
4
5
Range (R)
Trial Number
6
7
8
9
10
Range (R)
7. Calculate the average range of the projectile.
Average R ________ Meters
Uncertainty R (max – min)/2 _______meters
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Projectile Motion
8. Measure the height of the cannon muzzle above the ground.
Height _______________ meters
9. Use equation 2 along with your answers from steps 7 and 8 to calculate the initial
speed of the projectile. Show your work here
V0 ___________________________ Meters/Second
Part II - Predicting and Measuring Range for Different Launch Angles
During part one, we were launching the projectile from the table onto the floor. We were
also launching it horizontally each time. If, we launch the projectile so that it lands on the
table instead of the floor, we can use this equation to calculate its range. We can even
predict how far the projectile will go when we fire it at an angle instead of just shooting
straight.
In this case, the Range equals the horizontal component of the velocity (vx) multiplied by
the time in the air, so
R = vxt
Understanding how vx and t relate to the firing angle q (theta) and the initial speed vo
requires a bit of trigonometry, so we’ll leave out the derivation here. However, you can
see that the time in the air also depends on the vertical component of the velocity, and the
steeper the angle, the longer the projectile will spend in the air! However, there is a bit of
a compromise, as the horizontal component of the velocity gets smaller with steeper
angles.
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Projectile Motion
The final equation for the range as a function of initial velocity and firing angle is:
R=
vo2 sin 2θ
Equation 3
g
The symbol θ in this equation stands for the firing angle of the projectile.
Without making any calculations, what firing angle do you think will produce the longest
range?
1. Using equation 3 and your answer to question 9 in part I, predict the range for
several different angles and record them in the column labeled “Predicted R” on
the table below. Show your work for at least one angle here. Before you
calculate sin(2θ), do a quick check of your calculation skills and make sure that
sin(30o) = 0.5. If not, then your calculator needs to be set on degree mode.
θ
15◦
30◦
45◦
60◦
75◦
90◦
Predicted R
2. Point the cannon so that the projectile will land on the table. Set the angle to
fifteen degrees and fire once to see where the projectile lands.
3. Tape down a piece of scratch paper on the table where the projectile landed, and
tape a piece of carbon paper, carbon side down, on top of the scratch paper.
4. Fire the cannon three times. Lift up the carbon paper and measure the distance
from the cannon muzzle to each mark on your scratch paper. Record your
measurements in the table below.
5. Repeat steps 2-4 for all the other angles.
6. Calculate the average range for each angle and enter it in the final column
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θ
Range
Trial 1
15◦
30◦
45◦
60◦
75◦
90◦
Projectile Motion
Range
Trial 2
Range
Trial 3
Average R
7. Copy the results from the last two tables into the table below, and calculate the
percent difference between your measurements and your predictions for each
angle.
θ
Predicted R
Average
Measured R
15◦
30◦
45◦
60◦
75◦
90◦
Percent Difference
8. How close were your measurements to your predictions?
9. What angle produced the maximum range? Was it the angle you predicted
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Projectile Motion
Part III - Launching from the table to the floor at an angle
The last thing we’ll do tonight is turn the cannon around so that it is firing onto the floor
again. Instead of firing it horizontally, we will fire it at an angle.
What launch angle do you think will produce the maximum range? Why?
1. With the cannon facing away from the table, launch the projectile at an angle of
35◦ and measure the range. Repeat for launch angles of 45◦ and 55◦.
θ
35◦
45◦
55◦
Range
2. Which angle had the highest range? Does this match your prediction?
3. Now that you have finished the lab, write approximately two paragraphs
discussing what you did, how you did it, what you learned and how you would
interpret your results.
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