$A$ ship $X$ moving due north with speed $v$ observes that another ship $Y$ is moving due west with same speed $v$. The actual velocity of $Y$ is $........$.

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

An airplane airspeed indicator reads $100 \,m / s$ and its compass shows that it is heading $37^{\circ}$ east of north. The meteorological information provided to the navigator is that the wind velocity is $20 \,m / s$ towards east. The speed of the airplane relative to the ground is closest to ............ $\,m / s$

The velocities of $A$ and $B$ are $\vec{v}_A=2 \hat{i}+4 \hat{j}$ and $\vec{v}_B=3 \hat{i}-7 \hat{j}$ Velocity of $B$ as observed by $A$ is ..........

Figure shows two ships moving in $x-y$ plane with velocities $V_A$ and $V_B$. The ships move such that $B$ always remains north of $A$. The ratio $\frac{V_A}{V_B}$ is equal to ........

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