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 the north direction at a speed of $10 \ m/s$. $A$ parrot flies at a speed of $5 \ m/s$ towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is........$s$.

$A$ passenger train of length $60\, m$ travels at a speed of $80\, km/hr$. Another freight train of length $120\, m$ travels at a speed of $30\, km/hr$. The ratio of times taken by the passenger train to completely cross the freight train when:
$(i)$ they are moving in the same direction,and
$(ii)$ in the opposite directions is

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

$A$ man is running at a speed of $5 \, m/s$. The rain drops appear to be falling at an angle of $45^{\circ}$ from the vertical. If the rain drops are actually falling vertically downwards,then the velocity of the rain drops (in $m/s$) is:

$A$ 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).