A river is flowing from west to east at a speed of $8\,m$ per min. A man on the south bank of the river, capable of swimming at $20\,m / min$ in still water, wants to swim across the river in the shortest time. He should swim in a direction

A girl standing on road holds her umbrella at $45^{\circ}$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15 \sqrt{2} \; kmh ^{-1}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is ...........  $kmh ^{-1}$

The rebound coefficient between a tennis ball and a racket is defined as $g = v_2/ v_1$, where $v_1$ is the incoming speed of the ball and $v_2$ is the speed of the ball after rebound while the racket is at rest. A tennis ball falls from height $H$ to a racket at rest and bounces back to $0.8\  H. A$ tennis player is using the racket to hit an incoming tennis ball traveling at $150\ km/hr$ and the racket is moving at $100\ km/hr$. What is the speed of the ball after being hit? (Assume the mass of the racket >> that of the ball)..........$km/hr$

Aboat having a speed of $5\,\, km/hr$. in still water, crosses a river of width $1\,\, km$ along the shortest possible path in $15 \,\,minutes$. The speed of the river in $Km/hr.$

The width of river is $1\; km$. The velocity of boat is $5\; km/hr$. The boat covered the width of river with shortest will possible path in $15 \;min$. Then the velocity of river stream is

A boat crosses a river with a velocity of $8\, km/h$. If the resulting velocity of boat is $10 \,km/h $ then the velocity of river water is...........$km/h$