Relative Motion

Motion is always described relative to a frame of reference. There is no concept of 'absolute motion' in classical mechanics.

Relative velocity of A with respect to B: v_AB = v_A − v_B (vector subtraction).

In 1D, if objects move in the same direction, relative velocity is the difference; if in opposite directions, it is the sum.

The relative velocity determines how fast two objects approach or separate from each other.

In a moving frame, an observer sees the other object's velocity as the relative velocity — this simplifies many problems.

Rain-umbrella problems use relative velocity: tilt angle = tan⁻¹(v_man / v_rain).

River-boat problems: to cross in shortest time, row perpendicular; to cross shortest path, adjust angle upstream.

Relative motion analysis converts two-body problems into single-body problems — a powerful JEE problem-solving technique.