Walkthrough

Projectile motion, step by step

After it leaves your hand, the only force on a projectile is gravity. Walk the five steps from the method guide, then drag the launcher. Every readout uses g = 9.8.

  1. 01

    Split the motion into x and y

    Horizontal velocity stays constant. Vertical motion is free fall at g = 9.8 m/s^2. The two directions share only time.

  2. 02

    List the knowns by axis

    For an angled launch, vx0 = v0 cos theta and vy0 = v0 sin theta. Write a two-column table before touching an equation.

  3. 03

    Solve the vertical direction for time

    Time of flight always comes from y. A horizontal launch from height h uses t = sqrt(2h/g). Level ground uses symmetry: t = 2 vy0 / g.

  4. 04

    Multiply that time by the horizontal velocity

    Range is R = vx0 t. Do not start from the level-ground shortcut. That formula is not on the AP sheet and fails when heights differ.

  5. 05

    Combine components if asked for impact speed

    vx never changes. vy = vy0 - g t. Speed is the magnitude of those two. Then drag the launcher until the same numbers appear on the readout.

gravitym/s2, approximate
01020304050 m51015 mmax height 10.20 mrange 40.82 mvxvyv45°20.0 m/s
Range
40.82 m
Max height
10.20 m
Time of flight
2.89 s
Live at t = 0.00 s
20.00 m/s
vx 14.14, vy 14.14 m/s
x 0.00 m, y 0.00 m

Full method: how to solve projectile motion problems. Calculator: projectile motion calculator. Physics 1 cram sheet: units and weights.