To a stationary man, rain appears to be falling at his back at an angle ${30}^o$ with the vertical. As he starts moving forward with a speed of $0.5 \mathrm{m} {\mathrm{s}}^{-1},$ he finds that rain falls vertically. The speed of rain with respect to stationary man is

A river is flowing from east to west at a speed of $5 \mathrm{m} {\min }^{-1}$. A man on the south bank of river, capable of swimming $10 \mathrm{m} {\min }^{-1}$ in still water, wants to swim across the river in the shortest time. He should swim

 Two men, $P$ and $Q$ are standing at corners $A$ and $B$ of a square $ABCD$ of side $8 \mathrm{m}$. They start moving along the track with constant speed $2 \mathrm{m} {\mathrm{s}}^{-1}$ and $10 \mathrm{m} {\mathrm{s}}^{-1}$, respectively. Find the time when they will meet for the first time.