$2 \mathrm{km}$ wide river flowing at the rate of $5 \mathrm{km} {\mathrm{h}}^{-1}$. A man can swim in still water with $10 \mathrm{km} {\mathrm{h}}^{-1}.$ He wants to cross the river along the shortest path. Find in which direction should the person swim.

A child runs to and fro with a speed $9 \mathrm{km} {\mathrm{h}}^{-1}$ (with respect to the belt) on a long horizontally moving belt (figure) between $h$ is father and mother located $50 \mathrm{m}$ apart on the moving belt. The belt moves with a speed of $4 \mathrm{km} {\mathrm{h}}^{-1}$. For an observer on the stationary platform outside, what is the $\left(a\right)$ speed of the child running in the direction of motion of the belt and $\left(b\right)$ speed of the child running opposite to the direction of motion of the belt? $\left(c\right)$ time taken by the child in $\left(a\right)$ and $\left(b\right)$. Which of the answers will alter if motion is viewed by one of the parents?

Three particles $P, Q$ and $R$ are situated at point $A$ on the circular path of radius $10 \mathrm{m}.$ All three particles move along different paths and reach point
$B$ as shown in the figure. Then the ratio of the distance traversed by particles $P$ and $Q$ is: