A boy of mass `40 kg` moves on a `10 m` long , `60 kg` railroad car on the smooth horizontal floor. Now the boy moves with speed `5 m//s`. (a) Find the velocity of the car with respect to the floor. (b) If the boy starts from middle of the car and reaches to one end of the car , find the distance traveled by the car. (c ) If the boy stops at the end , find the velocity of the car. (d) If the boy falls off the car at one end while walking , find the velocity of the car.

Explanation

(a) Let `v` be the velocity of car w.r.t. the ground.
`v_(B//g) = ( 5 - v)`
Applying momentum conservation
`0 = 40(5 - v) - 60v rArr v = 2 m//s`
`(b)` When the boy reaches to the right end , the distance traveled by the car `x`, towards the left.
Distance traveled by the boy w.r.t. the ground `( 5 - x)`.
Since the location of `c.m`. is fixed
`40( 5 - x) = 60 x rArr x = 2m`
OR
`40 xx 5 = (60 + 40)x rArr x = 2 m`
( c) When the boy stops , the car (due to the conservation of momentum).
(d) When the boy falls at one end,
`O' = 40 (5 - v) - 60 v`
`v = 2 m//s`