Question

A man of mass $80\text{kg}$ jumps from a trolley of mass $20\text{kg}$ standing on a smooth surface, with an absolute velocity of $3\text{m/s}$. The recoiling speed of the trolley is

• A. $12\text{m/s}$
• B. $10\text{m/s}$
• C. $8\text{m/s}$
• D. $11\text{m/s}$

Answer 1

The correct option is A $12\text{m/s}$

Given:
Mass of man; $m_1=80\text{kg}$
Mass of trolley; $m_2=20\text{kg}$
Final velocity of man; $v_1=3\text{m/s}$
Initial velocity of man ($u_1$) and trolley ($u_2$) are zero as both are at rest. Let ($v_2$) be the final velocity of trolley.

Considering (man+trolley) as system. As there are no net external force in horizontal direction on the system.
$\therefore$ Applying principle of conservation of linear momentum (PCLM) in horizontal direction,
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$0=80\times 3+20\times v_2$
$v_2=-12$ $\text{m/s}$
Here negative (- ve) sign shows that trolley moves in the opposite direction of man.
$\therefore \text{Recoiling speed of trolley}=12\text{m/s}$