Question

A trolley is moving horizontally with a constant velocity of v with respect to earth. A man starts
running from one end of the trolley with a velocity 1.5 v with respect to trolley. After reaching the opposite end, the man returns back and continues running with a velocity of 1.5 v w.r.t. the trolley in the backward direction. If the length of the trolley is L then the displacement of the man with respect
to earth during the process will be :-​

Answer 1

Answer:

initial velocity of trolly = v

let when start running then velocity of trolly become =v1

 velocity of man with respect to earth = ( v1 + 3/2v)

conservation of momentum

(m+m)v = mv1  + m(v1 + 3/2v)

v1 =v/4

time taken by man to reach at the other end t1 = L /(3/2 v) =2L/3v

when starts moving in backward direction let velocity of trolly  =v2

then velocity of man w.r.t earth  = v2 - 3/2 v

conservation of momentum

(m+m)v = mv2  + m(v2 - 3/2 v)

v2 = 5v/4

time taken by man to reach at the initial  end t2 = L /(3/2 v) =2L/3v

so distance moved by trolly  = V1 t1  + V2 =v/4 * 2L/3v   +  5v/4 * 2L=L

Answer 2

Answer: 4L/3

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