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 Formula

Watch this tutorial for more information on Relative Velocity

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

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