Wind is blowing in the north direction at speed of $2 \,\,m/s$ which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him :

A girl standing at point $P$ on a beach wishes to reach a point $Q$ in the sea as quickly as possible. She can run at $6 \,kmh ^{-1}$ on the beach and swim at $4 \,kmh ^{-1}$ in the sea. She should take the path

Ram moves in east direction at a speed of $6 \,m / s$ and Shyam moves $30^{\circ}$ east of north at a speed of $6 \,m / s$. The magnitude of their relative velocity is ........ $m / s$

A swimmer wants to cross a river from point $A$ to point $B$. Line $A B$ makes an angle of $30^{\circ}$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $\theta$ with the line ${AB}$ should be $^{\circ}$, so that the swimmer reaches point ${B}$.

A $2\,m$ wide truck is moving with a uniform speed $v_0=8\,m / s$ along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed $v$ when the truck is $4 m$ away from him. The minimum value of $v$ so that he can cross the road safely is $...........\frac{m}{s}$

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)..........$km/hr$