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 Principle The 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 θ Vertical component (u_y): u_y = U θ The resulting path is a parabola .
Worked Example: Horizontal Projectile Question: 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? Solution 1. Vertical motion: Find time to fall 20 m.
s = 20, u_y = 0, a = 9.81. Use s = fractiongt^2 20 = 0.5 × 9.81 × t^2 t^2 = 4.077 t = 2.02 s 2. Horizontal motion: Use time to find distance. Range = u_x × t = 15 × 2.02 = 30.3 m
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