Relative velocity is one of those basic concepts in physics that helps us understand the speed and direction relation between two objects with regard to one another. Whether it is two cars on a highway or a boat navigating along a river, analyzing motion accurately absolutely depends on one knowing relative velocity.

Definition: Relative velocity is the velocity of one object while viewed from another moving object. It gives us how fast and in what direction one object is moving relative to another.

Formula 

Where,

VAB is the velocity with respect to A and B, VBC is the velocity with respect to B and C and VAC is the velocity with respect to A and C.

Solved Problems

Problem 1: A train travels with a speed of 70m/s with regards to the ground in the east direction. A spectator is moving with a speed of -15m/s with regards to the train in the west direction. Determine the speed of man with respect to the ground? 

Answer:

From the problem, it is known that

VBC (Velocity of the train with respect to ground) = 70m/s

VAB (Velocity of man with respect to train) = -15m/s

VAC (Velocity of a man with respect to ground) =?

Relative Velocity Formula is,

VAC→ = VAB→ + VBC→

VAC→ = -15+70 = 55m/s

VAC→ = 55m/s

Problem  2: A boat moves with a speed of 40m/s with respect to water in the east direction. An observer is moving with a speed of -5m/s with respect to the boat in the west direction. Compute the speed of man with respect to the water?

Answer:

From the problem, it is known that

VBC (Velocity of boat with respect to water) = 40m/s

VAB (Velocity of man with respect to boat) = -5m/s

(Velocity of a man with respect to water) VAC =?

Formula for relative velocity is,

VAC→ = VAB→+ VBC→

VAC→ = -5+40 = 35m/s

VAC→ = 35m/s

 

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