Question

A cart of mass $M=100kg$ is at rest over a smooth horizontal surface. A boy of mass $m=50kg$ is standing over the cart. If he jumps from the cart with a horizontal velocity of $20m{s}^{-1}$, the final velocity of the cart is :

• A. $10m{s}^{-1}$
• B. $20m{s}^{-1}$
• C. $-10m{s}^{-1}$
• D. $-20m{s}^{-1}$

Answer 1

The correct option is C $-10m{s}^{-1}$

Given:
Mass of boy $\left(m_1\right)$ = $50kg$
Mass of cart $\left(m_2\right)$ = $100kg$
Initial velocity of boy $\left(u_1\right)$ = $0m{s}^{-1}$
Initial velocity of cart $\left(u_2\right)$ = $0m{s}^{-1}$
Final velocity of boy $\left(v_1\right)$ = $20m{s}^{-1}$
Final velocity of cart $\left(v_2\right)$ = $?$
According to the law of conservation of momentum,
Initial momentum of the system = Final momentum of the system
$\Rightarrow$$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$\Rightarrow$$0+0=50\times 20+100\times v_2$
$\Rightarrow$ $v_2=-10m{s}^{-1}$

Negative sign indicates the velocity of cart is in opposite direction of the velocity of the boy.