# Relative Velocity Formula

RelativeÂ velocityÂ isÂ usedÂ toÂ denote theÂ aircraftÂ movingÂ inÂ theÂ windÂ orÂ boatsÂ movingÂ through theÂ water,Â etc.Â TheÂ velocityÂ isÂ measuredÂ withinÂ theÂ objectÂ accordingÂ toÂ theÂ observer.Â ItÂ canÂ beÂ measuredÂ usingÂ theÂ useÂ ofÂ anÂ intermediateÂ referenceÂ frame.Â  In simpler terms, this can be the vector sum of the velocities. The relative velocity formula is expressed as

$$\begin{array}{l}\vec{V}=\vec{V_{AB}}+\vec{V_{BC}}\end{array}$$

Where

VABÂ is the velocity with respect to A and B,Â VBCÂ is the velocity with respect to B and C andÂ VAC is the velocity with respect to A and C.

Relative Velocity Solved Examples

ProblemÂ 1:Â 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?Â

From the problem, it is known that

VBC (Velocity of train with respect to ground)Â = 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,

VACâ†’ =Â VABâ†’ + VBCâ†’

VACâ†’Â = -15+70 = 55m/s

VACâ†’ =Â 55m/s

ProblemÂ  2:Â 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

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

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

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

Formula for relative velocity is,

VACâ†’ =Â VABâ†’ + VBCâ†’

VACâ†’Â = -5+40 = 35m/s

VACâ†’ =Â 35m/s