Projectile Motion Calculator

Initial Velocity (m/s):

Launch Angle (degrees):

Initial Height (m):

Maximum Height: - m

Range: - m

Time of Flight: - s

Understanding Projectile Motion

What is Projectile Motion?

Projectile motion is a form of motion where an object moves in a curved path (parabola) under the influence of gravity alone.

Maximum Height: h = (v₀sinθ)²/(2g)

Range: R = (v₀²sin2θ)/g

Time of Flight: T = (2v₀sinθ)/g

where:

v₀ = initial velocity
θ = launch angle
g = acceleration due to gravity (9.81 m/s²)
h₀ = initial height

Advanced Concepts

Vector Components: Horizontal and vertical motion
Conservation of Energy: Kinetic and potential energy
Air Resistance: Real-world effects
Magnus Effect: Spinning projectiles
Optimal Angles: Maximum range conditions
Relative Motion: Moving reference frames
Coriolis Effect: Earth's rotation influence
Ballistic Coefficient: Mass and drag effects
Terminal Velocity: Air resistance equilibrium
Energy Dissipation: Non-conservative forces

Applications and Analysis

Sports Science

Ball games, athletics

Ballistics

Trajectory analysis

Space Science

Orbital mechanics

Engineering

Projectile design

Artillery

Range calculations

Video Games

Physics engines