Projectile Motion


In this lab you will study the motion of a freely-falling projectile, namely a small plastic sphere. Projectile motion, for our purposes, is the motion of an object that has been launched and then is subject to only the force of gravity and the force of air friction. The Newtonian mechanics principles that you have been studying allow you to predict this type of motion quite well. You will perform two experiments to aid your understanding of these principles, which will be described later in the lab. Since there is the small but real possibility of causing injury to yourself or another person, please follow all safety guidelines and common sense safety rules.

Time-of-flight vs. Initial Velocity

The purpose of this experiment is to determine whether the time-of-flight of a ball launched horizontally off the table varies as the initial velocity is varied. A ball launched horizontally from a table of height h has no initial velocity in the vertical direction, so the ball should take the same amount of time to reach the ground as a ball that drops from rest from the same height. The kinematic equation
h = (1/2)gt2 
can be used to determine the time-of-flight, which is independent of initial velocity:
( 1 )
t =
Figure 1

Figure 1

Projectile Motion

The purpose of this experiment is to predict and verify the range and the time-of-flight of a projectile launched at an angle.
Figure 2

Figure 2

To predict the range of the projectile when it is shot off a table at some angle above the horizontal, it is necessary first to determine the initial speed (muzzle velocity) of the ball. The initial velocity of the ball is determined by shooting it, at the appropriate angle, through 2 photogates that are placed near the muzzle and only a few centimeters apart from each other. Then the initial velocity can be used to calculate where the ball will land when it is shot at some angle θ. Initial velocity: The photogates are approximately 10 centimeters apart (measure directly to confirm this). A Smart Timer can be used to measure the time the ball takes to travel between these two gates. The average speed between the gates can then be calculated from v = (10 cm)/time. Time-of-flight and range: To predict the total time-of-flight, you can use the vertical y-component of the initial velocity along with the initial and final y-coordinates of the ball. To predict the range, you can use the total time-of-flight and the x-component of the initial velocity. You will derive these two equations, one for the range and one for the total time-of-flight, before you actually perform the experiment. Then, you will calculate values for the range and time-of-flight using your equations. After you calculate the expected values, you will perform the experiment to see if you calculated correctly!


General Operation of the Projectile Launcher

Safety glasses must be worn during this experiment.
When the projectile launcher is loaded, a yellow indicator is visible in one of the range slots in the side of the barrel and the ball is visible in another one of the slots in the side of the barrel. As with all projectile launching mechanisms, NEVER LOOK DOWN THE BARREL WHEN IT IS LOADED. To check to see if the launcher is loaded, always check the side of the barrel.
Before shooting the ball, make certain no one is in its flight path. To shoot the ball, pull straight up on the string that is attached to the trigger. It is only necessary to pull it about a centimeter.

Time-of-flight vs. Initial Velocity

Equipment Set-Up

The launchers should be set up when you arrive; do not adjust the placement of the launchers unless instructed to do so by your TA. Each launcher should be clamped to the edge of a lab bench and aimed so that the ball will land on the floor without hitting any other lab groups. Note: If the timer does not start, the photogate beam may be blocked by the launcher, in which case the bracket should be moved outward so that the first photogate is just beyond the front end of the launcher.


Whenever you launch a ball, position one member of your lab group ready to catch the ball after it lands to avoid losing the ball or interfering with other students in the room. You should observe that the time of flight does not depend on the initial velocity when the ball is launched horizontally. Calculate the initial velocity for each of the two launch settings from
vo = Δx/Δt
where Δx is the range or horizontal displacement of the ball.

Projectile Motion

Measuring the Initial Velocity Directly

Predicting and Verifying the Range and Total Time-of-Flight

Use the equations you derived in the Pre-lab Assignment to calculate the expected range and time-of-flight using your best estimate of the average initial velocity for the short range setting, and the launch angle. To test your predictions, follow the steps outlined below.

Target Challenge (optional)

For an additional challenge, your TA may place a target or basket at a specified point for you to try to hit. Use your equations to determine an appropriate launch setting to score a hit!


Time-of-flight vs. Initial Velocity

Projectile Motion


Did the time-of-flights for part one change with the initial velocity? Discuss the differences between your predicted and experimental results for both the range and time-of-flight. Is there agreement to within the uncertainties? If not, explain. Which is more significant for this lab: random or systematic errors? How can you tell? What do you believe is the primary source of uncertainty in this experiment? What would you do differently to improve your results? How significant is air resistance for this experiment? Use your experimental results to estimate the maximum relative error introduced by this factor.