All subjects · Physics · WPH11 (Unit 1)

Projectile motion

A projectile moves sideways and falls at the same time. The key is that horizontal and vertical motions are independent.

Independence

With no air resistance, the only force on a projectile is its weight, which acts vertically. So:

Time is the link between the two directions.

Horizontal launch

An object launched horizontally starts with zero vertical velocity. Use s = (1/2)gt2 vertically to find the time of flight, then horizontal distance = horizontal speed x time.

Launch at an angle

Resolve the launch velocity: u_h = u cos θ and u_v = u sin θ. Use suvat on the vertical motion to find the time (at the top, v_v = 0). Then range = u_h x total time. On level ground, the time to the top is half the total time of flight.

Worked example

A ball rolls off a table 1.25 m high at 3.0 m/s. How far from the table does it land?

  1. Vertical: 1.25 = 0.5 x 9.81 x t2, so t = sqrt(2.50 / 9.81) = 0.505 s
  2. Horizontal: distance = 3.0 x 0.505

Answer: It lands 1.5 m from the table.

Key idea: Split the motion: horizontal velocity constant, vertical acceleration g. Time links the two.

Check yourself

  1. Ignoring air resistance, what happens to the horizontal velocity of a projectile during its flight?
    • It increases
    • It stays constant
    • It decreases
    • It becomes zero at the top
    Show answer

    It stays constant. No horizontal force acts, so the horizontal velocity does not change.

  2. A stone is thrown horizontally from the top of a cliff 20.0 m high. How long does it take to reach the sea, in s? Give 3 s.f.
    Show answer

    2.02 s. 20.0 = 0.5 x 9.81 x t2, so t = sqrt(40.0 / 9.81) = 2.02 s.

  3. The stone in the last question was thrown at 15 m/s horizontally. How far from the foot of the cliff does it land, in m? Give 3 s.f.
    Show answer

    30.3 m. Distance = 15 x 2.019 = 30.3 m.

  4. A ball is kicked from level ground at 20 m/s at 30° above the horizontal. How long does it take to reach its highest point, in s? Give 3 s.f.
    Show answer

    1.02 s. u_v = 20 sin 30° = 10 m/s. At the top v_v = 0: t = 10 / 9.81 = 1.02 s.

  5. For the same kick (20 m/s at 30°, level ground), find the total time of flight in s, to 3 s.f.
    Show answer

    2.04 s. Total time = 2 x 1.019 = 2.04 s.

  6. For the same kick, find the horizontal range in m, to 3 s.f.
    Show answer

    35.3 m. u_h = 20 cos 30° = 17.32 m/s; range = 17.32 x 2.039 = 35.3 m.

  7. From the same height and at the same instant, ball A is dropped and ball B is thrown horizontally. Ignoring air resistance, which lands first?
    • They land at the same time
    • Ball A
    • Ball B
    • It depends on B's speed
    Show answer

    They land at the same time. Both start with zero vertical velocity and have the same vertical acceleration g.

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Last updated 7 November 2026. Spotted a mistake? Tell us.