This figure shows a man of mass `m` standing at the end `A` to a trolley of mass `M` placed at rest on a smooth horizontal surface. The man starts moving towards the end `B` with a velocity `u_(rel)` with respect to the trolley. The length of the trolley is `L`.

(a) Find the time taken by the man to reach the other end.
(b) As the man walk on the trolley, find the velocity centre of mass of the system (man+trolley).
(c) When the man reaches the end `B`, find the distance moves by the trolley with respect to ground.
(d) Find the distance moved by the man with respect to ground.

Answer

(a) `(L)/(u_("rel"))`
(b) zero
(c) `(mL)/(m+M)`
`(d) (ML)/(m+M)`