# Relative Velocity Formula

Relative velocity is used to denote the aircraft moving in the wind or boats moving through the water, etc. The velocity is measured within the object according to the observer. It can be measured using the use of an intermediate reference frame.  In simpler terms, this can be the vector sum of the velocities. The relative velocity formula is expressed as

$\overrightarrow{V}=\overrightarrow{V_{AB}}+\overrightarrow{V_{BC}}$

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.

Relative Velocity Solved Examples

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?

From the problem, it is known that

VBC (Velocity of 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?

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