Question

A man of $50 \, kg$ is standing at one end on a boat of length $25 \, m$ and mass $200 \, kg$ . If he starts running and reaches the other end, he has a speed $2 \, m \, s^{- 1}$ with respect to the boat. The final speed of the boat is ( in $\left.m s^{-1}\right)$

• A. $\frac{2}{5}$
• B. $\frac{2}{3}$
• C. $\frac{8}{5}$
• D. $\frac{8}{3}$

Answer 1

Answer: (A)

Let $v$ be the speed of the boat with respect to the water, then from conservation of linear momentum.
$-\left(200 + 50\right)v+50\times 2=50\times 0+200\times 0$
$250v=-100$
$v=-\frac{100}{250}=-\frac{2}{5} \, m \, s^{- 1}$