## Relative velocity Formula :

Relative velocity Formula V_{(m/s)} in meter per second is equal to the A and B respect with velocity v_{AB(m/s)} in meter per second and addition of t he B and C respect with velocity V_{BC(m/s)} in meter per second. Hence the Relative Velocity Formula can be written as

**V _{(m/s)}=v_{AB(m/s)}+V_{BC(m/s)}**

Where,

_{V→ velocity in m/s}

v_{AB} → velocity with respect A and B

V_{BC} → velocity with respect B and C

V_{AC} → e velocity with respect A and c

## Sample Sums :

### sum1 :

Calculate the speed of man with respect to the ground? A train travels with a speed of 90m/s with regards to the ground in the east direction. A spectator is moving with a speed of -20m/s with regards to the train in the west direction.

### Solution :

From the problem, it is known that

V_{BC} (velocity of train with respect to ground)=90m/s

v_{AB} (velocity of man with respect to train)=-20m/s

V_{AC} (velocity of a man with respect to ground)=?

Relative velocity formula is given by

V_{AC} → _{ }= v_{AB} → + V_{BC} →

V_{AC} → = -20+90=70m/s

V_{AC} → =70m/s

### Sum2 :

Calculate the speed of man with respect to the water? In a boat moves with a speed of 80m/s with respect to water in the east direction. An observer is moving with a speed of -35m/s with respect to the boat in the west direction.

### Solution :

The formula is given by

V_{BC} (velocity of boat with respect to water)=80m/s

v_{AB} (velocity of man with respect to boat)=-35m/s

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

Formula for relative velocity is

V_{AC} → _{ }= v_{AB} → + V_{BC} →

V_{AC} → _{ =-35+80=45m/s}

V_{AC} → _{ =45m/s}