Projectile Motion Learning App

Theory

What is Projectile Motion?

Projectile motion is the motion of an object thrown or projected into the air, subject only to acceleration as a result of gravity.

Key Equations

Horizontal motion: x = v₀cosθ × t
Vertical motion: y = v₀sinθ × t - ½gt²
Time of flight: T = (2v₀sinθ)/g
Maximum height: H = (v₀²sin²θ)/2g
Range: R = (v₀²sin2θ)/g

Parameters

v₀ = initial velocity (m/s)
θ = projection angle (degrees)
g = acceleration due to gravity (9.8 m/s²)
t = time (s)

Problem Solver

Initial Velocity (m/s)

Projection Angle (degrees)

Initial Height (m)

Visualization

Practice Problems

Problem 1

A ball is thrown with an initial velocity of 15 m/s at an angle of 30° to the horizontal. Calculate the maximum height reached and the horizontal distance traveled.

Problem 2

A stone is thrown from a cliff 20 meters high with a velocity of 25 m/s at 15° above the horizontal. How long does it take to hit the ground?

Problem 3

A projectile is launched at 60° with the horizontal and lands 100 meters away. What was the initial velocity?

Problem 4

At what angle should you throw a ball to achieve the maximum range? Prove mathematically.

Projectile Motion Master