 # Relative velocity

## 7. Relative velocity

• Consider two objects A and B moving with uniform velocities vAand vB along two straight and parallel tracks.
• Let xOAand xOB be their distances from origin at time t=0 and xAand xB be their distances from origin at time t.
• For object A
xA = xOA + vAt               (18)
and for object B
xB = xOB + vBt                (19)
subtracting equation 18 from 19
xB - xA = ( xOB - xOA ) + ( vB - vA) t                          (20)
• Above equation 20 tells that as seen from object A , object B seems to have velocity ( vB - vA) .
• Thus ( vB - vA ) is the velocity of object B relative to object A. Thus,
vBA = ( vB - vA )                (21)
• Similarly velocity of object A relative to object B is
vAB = ( vA - vB )                (22)
• If vB = vA then from equation 20
xB - xA = ( xOB - xOA )
i.e., two objects A and B stays apart at constant distance.
• vA > vB then (vB - vA ) would be negative and the distance between two objects will go on decreasing by an amount ( vA - vB ) after each unit of time. After some time they will meet and then object A will overtake object B.
• If vA and vB have opposite signs then magnitude of vBA or vAB would be greater then the magnitude of velocity of A or that of B and objects seems to move very fast.
• In short ### Relative velocity Conceptual questions

A. A gun is mounted on a train roof .Train is travelling with the velocity v in north direction.A car is also moving on a parallel track with train with velocity w in north direction.Two bullet are fired from the muzzle of the gun . Take north as positive and south as negative
1. Bullet one is fired in the north direction with the muzzle velocity $u$ . Find the velocity of the bullet as seen from the observer on the earth
a. $u+v$
b. $u-v$
c. $u$
d. $v$

2. find the velocity of the bullet as seen from the observer on the moving car
a. $u+v-w$
b. $u-v-w$
c. $u$
d. $v$

3.Second Bullet is fired in the south direction with the muzzle velocity $u$.Find the velocity of the bullet as seen from the observer on the earth
a. $u+v$
b. $v-u$
c. $u$
d. $v$

4.find the velocity of the second bullet as seen from the observer on the moving car
a. $u+v-w$
b. $v-u-w$
c. $u$
d. $v$

B. A train is moving in the west direction with a velocity 15m/s.A monkey runs on the roof of the train against its motion with a velocity 5m/s with respect to train .Take the motion along west as positive
5.Velocity of train relative to its driver
a. 0
b. 15 m/s
c. -15 m/s
d. 20 m/s

6. What is the velocity of train with respect to monkey
a. 5m/s
b -5 m/s
c. 15 m/s
d -15 m/s

7. find the velocity of monkey with respect to ground
a. 5 m/s
b. -5 m/s
c. 10 m/s
d. -10 m/s