Resolving motion into two perpendicular directions
Section: Kinematics | Syllabus: Cambridge AS Level Physics (9702)
Projectile Motion
Projectile motion occurs when an object is thrown or projected near the Earth's surface and moves along a curved path under the action of gravity only.
Key PrincipleThe horizontal and vertical components of motion are independent of each other.
Analyzing the Components
1. Horizontal Motion
- Force: No horizontal force (ignoring air resistance).
- Acceleration: Zero (a_x = 0).
- Velocity: Constant (v_x = u_x).
- Equation: Horizontal Distance = Horizontal Velocity × Time
2. Vertical Motion
- Force: Constant weight (W = mg) acting downwards.
- Acceleration: Constant acceleration downwards (a_y = g).
- Velocity: Changes uniformly.
- Equation: Use SUVAT equations (e.g., v_y = u_y + gt).
Resolving Initial Velocity
If an object is projected with initial velocity U at an angle θ to the horizontal:
Horizontal component (u_x): u_x = U cos θ
Vertical component (u_y): u_y = U sin θ
The resulting path is a parabola.
Worked Example: Horizontal ProjectileQuestion: A ball is kicked horizontally off a 20 m high cliff at 15 m s^-1. How far from the base of the cliff does it land?
Solution1. Vertical motion: Find time to fall 20 m.
s = 20, u_y = 0, a = 9.81. Use s = (1/2)gt^2
20 = 0.5 × 9.81 × t^2 t^2 = 4.077 t = 2.02 s2. Horizontal motion: Use time to find distance.
Range = u_x × t = 15 × 2.02 = 30.3 mInteractive revision notes, videos and practice questions load below.