Two persons, A of mass `60 kg` and `B` of mass `40 kg`, are standing on a horizontal platform of mass `50 kg`. The platform is supported on wheels on a horizontal frictionless surface and is initially at rest. Consider the following situations.

(i) Both `A` and `B` jump from the platform simultaneously and in the same horizontal direction.
(ii) A jumps first in a horizontal direction and after a few seconds `B` also jumps in the same direction. In both the situations above, just after the jump, the person (`A` or `B`) moves away from the platform with a speed of `3 m//s` relative to the platform and along the horizontal.
In situation (i), just after both `A` and `B` jump from the platform, velocity of centre of mass of the system (`A, B` and the platform) is

Options

A. `2m//s`
B. `6m//s`
C. `5m//s`
D. none of these

Answer

A

Explanation

When both jump simultaneously.

Let speed of the platform be `v`, then speed of `A` and `B` will be `3-v` as shown because relative velocity is `3 m//s`. conserving momentum is
`50v=(60+40)(3-v)`
`impliesv=2m//s`