Projectile Motion Simulator

A projectile is any object launched into the air that moves under gravity alone — a thrown ball, a fired shell, a jumping athlete. Horizontal and vertical motion are independent: gravity only pulls down, so the horizontal velocity never changes while the vertical velocity follows free fall. Change the launch speed and angle below, then watch the trajectory and readouts.

Initial speed 25 m/s

Launch angle 45 °

Range 63.7 mMax height 15.9 mFlight time 3.60 s

Controls

Initial speed: How fast the projectile leaves the launcher, in meters per second.
Launch angle: Angle above the horizontal at launch, in degrees.
Play / pause: Start, pause and resume the flight.
Reset: Return the projectile to the launcher.

The physics

R = \frac{v_0^2 \sin 2\theta}{g}

Range on flat ground

h = \frac{(v_0 \sin\theta)^2}{2g}

Maximum height

T = \frac{2v_0 \sin\theta}{g}

Time of flight

Assumptions

No air resistance
Flat ground — launch and landing at the same height
g = 9.81 m/s²
The projectile is a point mass

Guided activity

Set the angle to 30° and the speed to 25 m/s. Record the range, max height and flight time.
Keep the speed fixed and try 60°. Compare the range with the 30° result — what do you notice?
Try 45°. Explain why the range is largest here using the sin(2θ) term in the range equation.
Fix the angle at 45° and double the speed. By what factor does the range grow, and why?

Challenge questions

Can you find two different angles that give exactly the same range? Explain why using the range formula.
Which angle gives the greatest height, and why is it not the best angle for range?
If you could turn on air resistance, how would the optimal angle change?