Physics · Mathematical methods and mechanics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Kinematics describes motion without asking what causes it. Velocity is the rate of change of displacement (v = dx/dt) and acceleration is the rate of change of velocity (a = dv/dt). If the acceleration is constant, use the four standard equations. If it is not, differentiate or integrate.
On a position–time graph the gradient is the velocity. On a velocity–time graph the gradient is the acceleration and the area under the line is the displacement.
In projectile motion the horizontal and vertical motions are independent. The horizontal velocity stays constant and the vertical motion has acceleration g downwards. Relative velocity is found by vector subtraction.
Saying a projectile has zero speed at its highest point. Only the vertical component is zero there; the horizontal component u cos θ is unchanged, and the acceleration is still g downwards.
Answer: T = 3.0 s, H = 11.25 m, R ≈ 78 m.
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