Question

A flat car of mass $M$ is at rest on a frictionless floor with a child of mass $m$ standing at its edge. If child jumps off from the car towards right with an initial velocity $u$ with respect to the car, find the velocity of the car after its jump.

• A. $\frac{mu}{m+M}$
• B. $\frac{Mu}{m+M}$
• C. $\frac{mu}{m-M}$
• D. $\frac{Mu}{m-M}$

Answer 1

The correct option is A $\frac{mu}{m+M}$

Let car attains a velocity of magnitude $v$ leftwards, and the net velocity of the child with respect to earth will be $u-v$, as $u$ is its velocity with respect to the car. Initially. the system was at rest, thus according to momentum conservation momentum after jump must be zero, as

$m(u-v)=Mv$

$v=\frac{mu}{m+M}$

Hence, the velocity of the car after its jump is $v=\frac{mu}{m+M}$.