$A$ thief's car is moving with a speed of $10\,m/s$. $A$ police van chasing this car with a speed of $5\,m/s$ fires a bullet at the thief's car with a muzzle velocity of $72\,km/h$. Find the speed with which the bullet will hit the car in $m/s$.

$A$ bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane,the trajectory of the bomb is a:

$A$ jet airplane travelling at the speed of $500 \; km \; h^{-1}$ ejects its products of combustion at the speed of $1500 \; km \; h^{-1}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?

$A$ boy runs on a horizontal road with a speed of $4 \ m \ s^{-1}$ while it is raining. He sees that the rain is making an angle $\theta$ with the vertical while running from west to east. However,when he runs from east to west,the angle is $\alpha$. The rain is pouring down at an angle $45^{\circ}$ with the vertical and at a speed of $8 \ m \ s^{-1}$ as shown in the figure. The ratio $\frac{\tan \theta}{\tan \alpha}$ is,

When a car is at rest,its driver sees rain drops falling on it vertically. When driving the car with speed $v$,he sees that rain drops are coming at an angle $60^{\circ}$ from the horizontal. On further increasing the speed of the car to $(1+\beta)v$,this angle changes to $45^{\circ}$. The value of $\beta$ is close to...

$A$ man is crossing a river flowing with a velocity of $5 \ m/s$. He reaches a point directly across at a distance of $60 \ m$ in $5 \ s$. His velocity in still water should be: (in $m/s$)