$A$ 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?........$s$

An aeroplane is to go along a straight line from $A$ to $B$,and back again. The relative speed with respect to wind is $V$. The wind blows perpendicular to the line $AB$ with speed $v$. The distance between $A$ and $B$ is $\ell$. The total time for the round trip is:

Ship $A$ is moving westwards with a speed of $20 \ km h^{-1}$ and another ship $B$ which is at $200 \ km$ south of $A$ is moving northwards with a speed of $10 \ km h^{-1}$. The time after which the distance between them is shortest and the shortest distance between them are respectively

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 $\,km/h$)

$A$ boy standing on the footpath tosses a ball straight up and catches it. The driver of a car passing by,moving with uniform velocity,sees this. The trajectory of the ball as seen by the driver will be:

$A$ river is flowing with a velocity of $5 \ km/hr$ as shown in the figure. $A$ boat starts from $A$ and reaches the other bank. The width of the river is $b = 300 \ m$. The velocity of the boat in still water is $v_{br} = 3 \ km/hr$. If the boat aims to reach the point directly opposite to $A$ (point $B$),but due to the river flow,it reaches point $C$,what is the distance $AC$ covered by the boat? (Note: The boat is steered such that it maintains a straight path relative to the ground).