Question

A trolley of mass $200kg$ moves with a uniform speed of $36km/h$ on a frictionless track. A child of mass $20kg$ runs on the trolley from one end to the other ( $10m$ away) with a speed of $4m{s}^{-1}$ relative to the trolley in a direction opposite to its motion and jumps out of the trolley. What is the final speed of the trolley

• A. $8.4m{s}^{-1}$
• B. $10.4m{s}^{-1}$
• C. $12.2m{s}^{-1}$
• D. $14.6m{s}^{-1}$

Answer 1

Answer: (B)

$36km/h=36\times \frac{5}{18}m{s}^{-1}=10m{s}^{-1}$
$\left(m_T+m_C\right)u=m_T{v}_T+m_C{v}_C$
$(200+20)(10)=200v_T+20v_C$
$v_C=v_{CT}+v_{TG}$
$C$ -Child, $T$ -Trolley, $G$ -Ground $v_C=-4+10=6m{s}^{-1}$
$\Rightarrow (220)(10)-(20)(6)=200v_T$ or $v_T=10.4m{s}^{-1}$