For the two given particles $A$ and $B$ as shown in the figure,how much time will it take for their horizontal separation to become zero?

$A$ person running horizontally observes that rain is falling on his head vertically with a speed of $10\,m/s$. When he stops,he observes that the rain is falling at an angle of $30^o$ with the vertical. Find the speed with which the man was running.

Two trains,each of length $100 \, m$,are moving parallel towards each other at speeds of $72 \, km/h$ and $36 \, km/h$ respectively. In how much time will they cross each other (in $, s$)?

$Assertion$ : The magnitude of velocity of two boats relative to the river is the same. Both boats start simultaneously from the same point on one bank and may reach the opposite bank simultaneously while moving along different paths.
$Reason$ : For boats to cross the river in the same time,the component of their velocity relative to the river in the direction normal to the flow should be the same.

Rain is falling vertically with a speed of $30\; m/s$. $A$ woman rides a bicycle with a speed of $10\; m/s$ in the north to south direction. What is the direction in which she should hold her umbrella?

$A$ boy throws a ball in the air at $60^{\circ}$ to the horizontal,along a road with a speed of $10 \, m/s$. Another boy sitting in a passing car observes the ball. Sketch the motion of the ball as observed by the boy in the car,if the car has a speed of $18 \, km/h$. Give an explanation to support your diagram.