Dart Gun Lab
Introduction: Projectile Motion is used to describe that path of an object takes when airborne
and only having the force of gravity influence it’s action. Since gravity tries to pull objects
toward the center of the Earth, it affects only the object’s vertical motion. The horizontal and
vertical motions are independent of one another. This means that two objects dropped from the
same height (neglecting air resistance) should reach the ground at the same time.
If we know the initial velocity of a projectile and the angle at which it is launched, we
can calculate its horizontal and vertical displacements as well as the time it takes to hit the ground
or another object. We can also use these variables to calculate the projectile’s initial velocity.
Part A
Purpose: To find the theoretical time and horizontal velocity of a dart shot horizontally from a
table top.
Procedure:
1. Hold the dart gun level and shoot the dart horizontally from that height. Record this height in
meters.
2. Have your lab partner time how long it takes the dart to reach the ground.
3. Measure the horizontal displacement of your dart.
(This is your actual horizontal displacement.)
3. Do three trials.
Trial
Height
(meters)
Range
(meters)
Measured Time
(seconds)
Average
Part B:
Purpose: To see how launch angle affects the height and range of a projectile.
Procedure:
1. By using a protractor, position the dart gun so that it launches the dart at the following angles:
25o, 45o and 70o.
2. Measure the horizontal displacement.
3. Have your lab partner time how long it takes the dart to reach the ground.
4. Do three trials for each angle.
Angle (degrees)
Time of flight (seconds)
Horizontal Displacement
(meters)
25o
25o
25o
average
45o
45o
45o
average
70o
70o
70o
average
Part A: Calculations
1. Calculate the theoretical time of flight You can do this by using the equation:
dy = ½ a y t2
dy = vertical displacement (height)
ay = -9.81 m/s2
2. Calculate the theoretical initial horizontal velocity. You can do this by using the equation:
dx = v xt
dx = horizontal displacement
Part B: Calculations
1. Calculate the initial theoretical horizontal and vertical velocities of the projectile shot form
you dart gun. Show your work. Use vx from part A.
Horizontal velocity
vx = cos θ vx
Vertical velocity
vy = sin θ vy
2. Calculate the maximum theoretical height at each angle by using the equation:
dy = sin vy θ t + ½ a y t2
Part A analysis:
1. Compare the actual time to the theoretical time. Explain why they are different.
2. What two variables are necessary to calculate the initial velocity of the dart? How did you
obtain the data necessary to calculate the horizontal velocity?
3. Do you think that this is the actual horizontal velocity of the dart? Explain why or why not.
4. How could you obtain a more accurate measure of the initial horizontal velocity?
Part B analysis:
1. Graph the launch angle with the horizontal displacement. Identify the dependent and
independent variables.
2. Graph the launch angle with the vertical displacement. Identify the dependent and independent
variables.
3. How does the launch angle affect the horizontal displacement? Explain why.
4. How does the launch angle affect the vertical displacement? Explain why.
5. Which launch angle gives you the largest horizontal displacement? Explain why.
6. Which launch angle gives you’re the smallest vertical displacement? Explain why.
7. Discuss some sources of error that would cause your data not reflect the actual value.