Projectile Motion
Calculate range and height of projectiles. Enter values for instant results with step-by-step formulas.
Formula
R = vยฒsin(2ฮธ)/g
Range depends on initial velocity squared and the sine of twice the launch angle.
Worked Examples
Example 1: Cannonball
Problem:100m/s at 45ยฐ
Solution:100^2 / 9.81
Result:Range: 1019m
Frequently Asked Questions
What is projectile motion?
Motion of an object thrown into the air, subject only to gravity (ignoring air resistance).
Does mass affect projectile motion?
No, in a vacuum, mass does not affect range or time of flight (Galileo\'s insight).
What are Newton's three laws of motion?
Newton's first law states that an object at rest stays at rest and an object in motion stays in motion unless acted on by an external force. The second law relates force, mass, and acceleration: F = ma. The third law states that for every action there is an equal and opposite reaction.
How do I calculate projectile motion?
Break projectile motion into horizontal and vertical components. Horizontally, velocity is constant (x = v0*cos(theta)*t). Vertically, gravity accelerates the object (y = v0*sin(theta)*t - 0.5gt^2). Range = v0^2*sin(2*theta)/g. Maximum height occurs when vertical velocity equals zero.