$A$ person climbs up a stalled escalator in $60\,s$. If standing on the same but escalator running with constant velocity,he takes $40\,s$. How much time is taken by the person to walk up the moving escalator?........$s$

If a $100 \,m$ long train needs $7.2 \,s$ to cross an object moving in a direction opposite to the train's direction with a speed of $5 \,km/h$, then find the velocity of the train. (in $\,km/h$)

Rain is falling vertically with a speed of $30 \,m/s$. A man rides a bicycle with a speed of $10 \,m/s$ from East to West direction. At what angle with the vertical does he see the rain falling?

$A$ 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 $\,s$)

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54 \; km \; h^{-1},$ and train $B$ moves south with a speed of $90 \; km \; h^{-1}.$ What is the velocity of $B$ with respect to $A$?

$A$ 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,