Relative Motion
Visualize how motion appears different from different frames of reference. Understand relative velocity with interactive scenarios.
Key Notes
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.
Formulas
Relative Velocity
Velocity of A as seen by B.
Relative Acceleration
Acceleration of A relative to B.
Closest Approach
Minimum distance between two objects.
Time of Closest Approach
Time when distance is minimum.
River Crossing (shortest time)
Row perpendicular to the bank.
River Crossing (shortest path)
Angle upstream for zero drift.
Important Points
In the frame of one object, the other moves with relative velocity — this turns projectile-meets-projectile into a straight-line problem.
Relative velocity is frame-independent: v_AB measured by any inertial observer gives the same result.
For collision problems, relative velocity of approach = relative velocity of separation × coefficient of restitution.
In 2D relative motion, draw the velocity triangle: v_A = v_B + v_AB.
When two objects have equal velocities, relative velocity is zero — they appear stationary to each other.
JEE tip: always check if the problem simplifies in a non-ground frame before solving in the ground frame.
Relative Motion notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.