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. `7.5m//s`
B. `5.5m//s`
C. `4.5m//s`
D. `2.5m//s`

Answer

D

Explanation

After `A` jumps:

`(50+40)v_(1)=60(3-v_(1))impliesv_(1)=1.2m//s`
After Bjumps

`(50+40)v_(1)=50v_(2)-40(3-v_(2))`
`implies90xx1.2=50v_(2)-120+40v_(2)`
`impliesv_(2)=228/90=2.53m//s`