Projectile Motion | Interactive Physics model

Interactive experiment

Cannon ballTargetTrajectory

Target distance x (m) Target height h (m) Launch speed v₀ (m/s) Angle θ (degrees)

Time0.000 s

Ball x0.00 m

Ball y0.00 m

At target x--

Set the target and launch parameters, then press Fire.

Projectile Motion Python Simulation

This Python model calculates the motion of a projectile using its launch velocity, launch angle and gravitational acceleration. Change the parameters and compare the calculated trajectory, range and flight time with the interactive simulation above.

import math

# Target
x_target = 50.0     # horizontal distance (m)
h_target = 10.0     # target height (m)

# Cannon
v0 = 25.0           # initial velocity (m/s)
theta_deg = 35.0    # launch angle (degrees)

g = 9.81            # gravity (m/s^2)

theta = math.radians(theta_deg)

vx = v0 * math.cos(theta)
vy = v0 * math.sin(theta)

# Time when projectile reaches target x
t = x_target / vx

# Projectile height at target x
y = vy * t - 0.5 * g * t**2

# Difference from centre of target
error = y - h_target

print("Time at target =", round(t, 3), "s")
print("Projectile height =", round(y, 3), "m")
print("Target height =", h_target, "m")
print("Vertical error =", round(error, 3), "m")

tolerance = 1.0

if abs(error) <= tolerance:
    print("HIT!")
elif error > 0:
    print("MISS - projectile is too high")
else:
    print("MISS - projectile is too low")

How Does Projectile Motion Work?

Projectile motion combines horizontal motion with vertical motion under gravity. The horizontal velocity remains constant when air resistance is ignored, while gravity accelerates the projectile downward.

Launch Angle, Range and Maximum Height

Experiment with different launch angles and velocities to see how they affect the projectile's range, maximum height and time of flight.

Challenge: Keep the target at x = 50 m and h = 10 m. Adjust either the launch speed or angle until the cannon ball hits the target.