Projectile Motion Experiment Calculator — Find Launch Velocity and Angle from Your Measurements

About the Projectile Motion Experiment Calculator

In this projectile motion experiment calculator, you will build a simple launcher and explore the principles of parabolic projectile motion. After taking the measurements of a few launches, you will determine the velocity of the projectile — and you will then be able to predict the flight path for different launch angles and launch heights.

The neat thing about this calculator is that it works in reverse. For the experiment you enter the time of flight, the horizontal distance, and the initial height, and the calculator finds the launch angle and initial velocity for you. It supports both the American (imperial) and metric measurement systems.

Learning objectives

By participating in this experiment, you will:

• Learn the definition and basic concepts of projectile motion;
• Become familiar with the projectile motion equations;
• Gain an intuitive understanding of how initial velocity, projectile range, time of flight, and launch angle are related; and
• Demonstrate best practices in lab safety.

Please note that it is easiest to complete this experiment with a partner, although this is not strictly necessary.

Background: What is projectile motion?

Imagine an archer sending an arrow into the air. It starts moving up and forward, at some inclination from the ground. The further it flies, the slower its ascent is — until it finally starts descending, moving now downwards and forwards and finally hitting the ground again. If you could trace its path, it would be a curve called a trajectory in the shape of a parabola (ignoring air resistance). Any object moving in such a way is in projectile motion.

In this experiment, we will only consider the one major force acting on a projectile — the force of gravity. Air resistance is ignored. If you drew a free-body diagram of such an object, you would only have to draw one downward vector and denote it as “gravity.”

Depending on your learning objectives, you can either use the calculator alone or use the equations to try to work out the answers independently.

Materials

To make the launcher we recommend, you will need:

• A flat exercise band (light resistance is best), such as TheraBand;
• A rubber bouncy ball;
• A four-legged chair; and
• A magazine holder or other reference object (optional).

To measure the trajectory, you will need:

• A measuring tape or meter stick;
• Masking tape;
• A marker;
• A stopwatch or a smartphone that can take videos; and
• Goggles or glasses for eye safety.

Methods

1. Clear the pathway. Before setting up the launcher, clear the launch pathway. Ensure there are no windows, mirrors, or breakable objects in the line-of-sight. An open space or hallway 6 to 7 meters long gives you enough room. Alert anyone nearby so they don't accidentally walk in front of the launcher.
2. Set up the projectile launcher. Place the chair at one end of the launch pathway. Tie the resistance band across the two front legs of the chair using a regular overhand knot, secured with a slip knot so it is easy to undo later. Tie it so there is no slack — you want the band to be a straight line all the way across, without twists, so the projectile flies smoothly.
3. Practice launching the projectile. Pull the ball back into the band and release to fire it down the pathway. Practice until your launches are consistent in both distance and direction.
4. Measure and record. For each launch, measure the horizontal distance the ball travels and the height it was released from, and time how long it stays in the air (a slow-motion video helps). Repeat several times and average your results.
5. Calculate. Enter your averaged time of flight, distance, and launch height above. The calculator returns the initial velocity and launch angle of your projectile.

Projectile motion equations

Given the measured horizontal distance d, time of flight t, and launch height h, with gravity g (9.81 m/s² metric, 32.174 ft/s² imperial):

Discussion questions

• How consistent were your launches? What sources of error could explain the spread in your measurements?
• How would the launch angle change if you fired the same ball from a higher starting point but it landed at the same distance?
• The model ignores air resistance. Would the real launch velocity be higher or lower than the value the calculator reports? Why?
• Using your measured velocity, predict the range for a 45° launch from the ground. How does it compare to your experimental distance?

Metric vs American units

Quantity	Metric (SI)	American (US)
Distance / Height	m (metres)	ft (feet)
Velocity	m/s (metres per second)	ft/s (feet per second)
Gravity (g)	9.81 m/s²	32.174 ft/s²
Time	seconds (s)	seconds (s)
Angle	degrees (°)	degrees (°)

FAQs

• How does the calculator find the velocity and angle? — It uses your three measurements (time, distance, height) to solve the projectile motion equations in reverse: the horizontal velocity comes from Vx = d/t and the vertical velocity from Vy₀ = g·t/2 − h/t. Combining them gives the launch speed and angle.
• Do I need a partner? — Not strictly, but it is much easier — one person launches while the other records the time and marks the landing point.
• Why is my computed velocity different from a friend's? — Launch power, release height, and timing all vary between people and between shots. Averaging several launches improves accuracy.
• Does the projectile's mass matter? — No. Ignoring air resistance, all objects fall at the same rate, so mass does not appear in the equations.
• What gravity value is used? — 9.81 m/s² for metric and 32.174 ft/s² for imperial — the standard Earth surface values.
• Is air resistance included? — No. This calculator uses the idealised model that neglects drag, so real launches will fly a little shorter than predicted.