Question

A truck of mass $M$ is at rest on a frictionless road. When a monkey of mass $m$ starts moving on the truck in forward direction, the truck recoils with a speed $v$ backward on the road, with what velocity is the monkey moving with respect to truck?

Answer 1

Given,

Momentum of truck, $=MV$

Momentum of monkey, $=mv$

From conservation of momentum

Initial momentum =final momentum

$0=MV+mv$

$V=\frac{-mv}{M}$

Relative velocity of monkey with truck

$V_{relative}=v-V=v-\frac{-mv}{M}=v\left(\frac{M+m}{M}\right)$

Relative velocity is $v\left(\frac{M+m}{M}\right)$