$A$ 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 $m/s$.

Two particles $A$ and $B$ start moving from the origin in the $xy$-plane. Particle $A$ moves with a velocity of $20 \, m/s$ along the $x$-axis,and particle $B$ moves with a velocity of $30\sqrt{2} \, m/s$ at an angle of $45^{\circ}$ with the $x$-axis. The relative velocity of $B$ with respect to $A$ is ........... $m/s$.

Two particles are moving along two long straight lines,in the same plane,with the same speed $= 20 \, cm/s$. The angle between the two lines is $60^{\circ}$,and their intersection point is $O$. At a certain moment,the two particles are located at distances $3 \, m$ and $4 \, m$ from $O$,and are moving towards $O$. Subsequently,the shortest distance between them will be

$A$ swimmer can swim in still water with speed $v$ and the river is flowing with velocity $v/2$. To cross the river in the shortest distance,the swimmer should swim at an angle $\theta$ with the upstream. What is the ratio of the time taken to swim across in the shortest time to the time taken to swim across the shortest distance?

Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. $A$ girl is driving a scooty with a speed of $60 \ km/h$ in the direction $X$ to $Y$ and notices that a bus goes past her every $30$ minutes in the direction of her motion,and every $10$ minutes in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.

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