Skip to content

Projectile motion calculator

Range, maximum height and flight time of something launched at a speed and angle, from any starting height.

Favorite

Results

Range 40.79 m

How it works

x = v cos θ · t · y = h + v sin θ · t − ½ g t²

Split the launch speed into a sideways part (v × cos θ), which stays constant, and an upward part (v × sin θ), which gravity slows down and reverses. The flight lasts until the height comes back to the ground; the range is the sideways speed times that time. On flat ground 45° gives the longest throw; from a height, a slightly lower angle does.

  1. Split the speed vx = 20 × cos 45° = 14.1421 m/s · vy = 20 × sin 45° = 14.1421 m/s
  2. Time until it lands (14.1421 + √(14.1421² + 2 × 9.80665 × 0)) ÷ 9.80665 = 2.88 s
  3. Range = sideways speed × time 14.1421 × 2.88 = 40.79 m
  4. Highest point 0 + 14.1421² ÷ (2 × 9.80665) = 10.2 m

Good to know

  • Ideal physics: no air resistance, friction or spin unless an input says otherwise.

Printed from rocketcalc.io/physics/projectile-motion