Two cars $A$ and $B$ are moving in the same direction along a straight line with speeds $100 \text{ km/h}$ and $80 \text{ km/h}$, respectively, such that car $A$ is moving ahead of car $B$. $A$ person in car $B$ throws a stone with a speed $v$ so that it hits car $A$ with a speed of $5 \text{ m/s}$. The value of $v$ is . . . . . . $\text{km/h}$.

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

The speed of a swimmer in still water is $20 \; m/s$. The speed of river water is $10 \; m/s$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path,the angle at which he should make his strokes with respect to north is given by ......$^o$ west.

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

$A$ moves with $65 \, km/h$ while $B$ is moving in the same direction as $A$ with $80 \, km/h$. The relative velocity of $B$ with respect to $A$ is ......... $km/h$.

There are two particles $P$ and $Q$ separated by a distance of $10 \ km$ and moving with velocities of $10 \ kmph$ as shown in the figure. The time elapsed before they reach their minimum separation is.........$hr$.