Question

A train is moving southwards with a speed of 30ms^-1. A man is running on the roof of the train with speed of 5ms^-1 with respect to the train. Find the velocity of the man as observed by the person on the ground if the man is running

1. southwards

2. northwards.

Answer 1

If v_A and v_B are the velocity of the two bodies moving along the same direction with respect to the ground, relative velocity of A with respect to B is given by,

V_AB = V_A – V_B …………. (1)

Here, the velocity of the man with respect to the train,

v_AB = 5ms^-1 

velocity of the train with respect to the ground is,

v_B = 30 ms-1

∴ velocity of the man with respect to the ground,

v_A = v_B + v_AB = 30 + 5 = 35 ms^-1 if the man moves southwards. 

On the other hand, if the man moves northwards,

v_AB = – 5 ms^-1

∴ V_A = V_B – V_AB

= 25 ms^-1