Question

A trolley of mass $\text{M}=150\text{kg}$ is at rest over a smooth horizontal surface. Two boys each of mass $\text{m}=50\text{kg}$ are standing over the trolley. If they jump from the trolley with a relative velocity ${\text{v}}_r=20\text{m/s}$ (relative to the velocity of trolley just after jumping) one after other in same direction. The final recoil speed of trolley is

• A. 6 m/s
• B. 8 m/s
• C. 9 m/s
• D. 12 m/s

Answer 1

The correct option is C 9 m/s

Let ${\text{v}}_1$ be the velocity of trolley when the first boy jumps


As there are no net external force in horizontal direction.
$\therefore$ Applying PCLM,
$p_i=p_f$
$0=\text{m}({\text{v}}_r-{\text{v}}_1)-(\text{M}+\text{m}){\text{v}}_1$
$\Rightarrow {\text{v}}_1=\frac{{\text{mv}}_r}{\text{M}+\text{2m}}...\left(i\right)$

Now the 2${}^{nd}$ boy jumps, let ${\text{v}}_2$ be the velocity of trolley.


Again there are no external force in horizontal direction
$\therefore$Applying PCLM,
$p_i=p_f$
$-(\text{M}+{\text{m)v}}_1=\text{m}({\text{v}}_r-{\text{v}}_2)-{\text{Mv}}_2$
$\Rightarrow {\text{v}}_2=\left(\frac{\text{m}}{\text{M+m}}\right){\text{v}}_r+{\text{v}}_1\left(ii\right)$
$\therefore \text{Using equation (i) and (ii)}{\text{v}}_2={\text{mv}}_r[\frac{1}{\text{M+m}}+\frac{1}{\text{M+2m}}]$
$=50\times 20[\frac{1}{200}+\frac{1}{250}]$
$=9$ m/s