Projectile motion · Grade 12
A projectile is anything thrown or launched that then moves under gravity alone. The trick is to split the motion into two independent parts: horizontally the velocity stays constant, while vertically the object accelerates downwards at 9.8 m/s², just like a dropped ball. Vertical projectiles (thrown straight up) use only the vertical part.
Key facts
- Ignoring air resistance, horizontal velocity is constant and the acceleration is 9.8 m/s² downwards.
- Horizontal and vertical motions are independent; they share only the time.
- Launch at speed u, angle θ: uₓ = u cos θ, u_y = u sin θ.
- At the top of the path the vertical velocity is zero.
- On level ground: time of flight = (2u sin θ)/g; range = (u² sin 2θ)/g (greatest at 45°).
- Speed at any moment = √(vₓ² + v_y²).