Question

A girl of mass $40kg$ jumps with a horizontal velocity of $5m{s}^{-1}$ onto a stationary cart with frictionless wheels. The mass of the cart is 3 kg. What is her velocity as the cart starts moving? Assume that there is no external unbalanced force working in the horizontal direction.

Answer 1

$\text{Step 1: Initial \& final situation [Ref. Fig.]}$

$\text{Step 2: Momentum conservation}$

Let $V$ be the final velocity of the system and the girl.

Since there is no net external force, therefore applying momentum conservation

Considering rightward direction as positive; we can write.

$P_i=P_f$

$\Rightarrow M{u}_2+m{u}_1=(M+m)V$

$\Rightarrow V=\left(\frac{m{u}_1}{M+m}\right)=\left(\frac{40\left(kg\right)\times 5\left(m/s\right)}{40\left(kg\right)+3\left(kg\right)}\right)$

$\Rightarrow V=\frac{200}{43}m/s$

Hence the final velocity is $\frac{200}{43}m/s$