Question

suppose on a trolley(mass =M) which is initially at rest two men each of mass m are standing.. in first case both of them jump with velocity u relative to trolley and in the second case they jump one after the other... my question is why in the second case the velocity of the trolley is more than in the first case ... assume no friction or air drag.....

Answer 1

The velocities are same. Are you sure about them different?

Answer 2

\[v=\frac{-2mu}{M}\]

Answer 3

yes... velocity of the trolley is more when the two jump one after the other each with relative velocity u..

Answer 4

It's trivial to use the momentum conservation law to show that the first case is so so I'll try to give the second case.

First it's \((2m+M)0=(m+M)v+mu \),
So, \(v_1=\frac{-mu}{m+M}\)
Second its \((m+M)v_1=mu+Mv_2 \)
substituting and rearranging,
\(v_2 = \frac{-2mu}{M}\)
Is there something here that I missed?