# Relative Velocity Formula

Relative velocity is used to describe the motion of airplanes in the wind or moving boats through water etc. This velocity is computed according to the observer inside the object. This can be computed by introducing an intermediate frame of references. In simpler words, this can be the vector some of the velocities. Formula for relative velocity is articulated as,

Where,

V_{AB} is the velocity with respect to A and B, V_{BC} is the velocity with respect to B and C and VACVAC is the velocity with respect to A and C.

**Relative Velocity Solved Examples**

Let us converse upon the problems of relative velocity for better comprehension.

**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 west direction. Compute the speed of man with respect to the ground?

**Answer:**

From the problem, it is known that

V_{BC} (Velocity of train with respect to ground) = 70m/s

V_{AB} (Velocity of man with respect to train) = -15m/s

V_{AC} (Velocity of man with respect to ground), = ?

Relative Velocity Formula is,

V_{AC}→ = V_{AB}→ + V_{BC}→

V_{AC}→ = -15+70 = 55m/s

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

**Answer:**

From the problem, it is known that

V_{BC} (Velocity of boat with respect to water) = 40m/s

V_{AB }(Velocity of man with respect to boat) = -5m/s

(Velocity of man with respect to water) V_{AC} = ?

Formula for relative velocity is,

V_{AC}→ = V_{AB}→ + V_{BC}→

V_{AC}→ = -5+40 = 35m/s