$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \, km/h$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the moving man will be:

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days,if she remains stationary on the moving escalator,then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be

On a long horizontally moving belt,a child runs to and fro with a speed $9 \, km \, h^{-1}$ (with respect to the belt) between his father and mother located $50 \, m$ apart on the moving belt. The belt moves with a speed of $4 \, km \, h^{-1}$. For an observer on a stationary platform,the speed of the child running in the direction of motion of the belt is ..... $km \, h^{-1}$.

On a long horizontal belt,a child runs to and fro with a speed of $9\,km/h$ (with respect to the belt) between his father and mother located $50\,m$ apart on the moving belt. The belt moves with a speed of $4\,km/h.$ For an observer on the platform,the speed of the child in the direction of motion of the belt is.........$km/h$.

$A$ swimmer can swim in still water with $5 \,m/s$. If a river is flowing with $4 \,m/s$, then find the time to cross the river of width $300 \,m$ if he has to reach the exactly opposite point.

$A$ man can swim with a speed of $4.0 \; km/h$ in still water. How long does he take to cross a river $1.0 \; km$ wide if the river flows steadily at $3.0 \; km/h$ and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?