$A$ train of $150 \,m$ length is going towards north direction at a speed of $10 \,ms^{-1}$. $A$ parrot flies at the speed of $5 \,ms^{-1}$ towards south direction parallel to the railway track. The time for which the parrot flies alongside the train is (in $\,s$)

On a long horizontally moving belt,a child runs to and fro with a speed $9 \; km \; h^{-1}$ (with respect to the belt) between his father and mother located $50 \; m$ apart on the moving belt. The belt moves with a speed of $4 \; km \; h^{-1}$. For an observer on a stationary platform outside,what is the:
$(a)$ speed of the child running in the direction of motion of the belt?
$(b)$ speed of the child running opposite to the direction of motion of the belt?
$(c)$ time taken by the child in $(a)$ and $(b)$?
Which of the answers alter if motion is viewed by one of the parents?

Two particles $P_1$ and $P_2$ are moving with velocities $v_1$ and $v_2$ respectively. Which of the following statements about their relative velocity $v_{12}$ is true?

Car $A$ is moving to the East with a speed of $30 \text{ km/h}$, and car $B$ is moving to the North with the same speed. What is the velocity of car $B$ as measured from car $A$?

$A$ 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 $m/s$)

$A$ car travels with a speed of $40 \text{ km h}^{-1}$. Rain drops are falling at a constant speed vertically. The traces of the rain on the side windows of the car make an angle of $30^{\circ}$ with the vertical. The magnitude of the velocity of the rain with respect to the car is