$A$ person walks up a stalled escalator in $80 \,s$. When standing on the same escalator, now moving, he is carried up in $20 \,s$. The time taken by him to walk up the moving escalator is (in $\,s$)

$A$ slider block $A$ moves downward at a speed of $v_A = 2 \ m/s$,at an angle of $75^\circ$ with the horizontal as shown in the figure. The velocity of the portion of belt $B$ between ideal pulleys $C$ and $D$ with respect to $A$ is $v_{CD/A} = 2 \ m/s$ at an angle $\theta$ with the horizontal. The magnitude of the velocity of portion $CD$ of the belt when $\theta = 15^\circ$ is .......... $m/s$.

Two cars $A$ and $B$ are moving with speeds $v_A = 120 \text{ km/h}$ and $v_B = 50 \text{ km/h}$ respectively in the directions as indicated by the arrows in the figure below. What is the relative speed of car $B$ with respect to car $A$ (in $\text{ km/h}$)?

Rain is falling vertically with a speed of $35 \; m s^{-1}$. $A$ woman rides a bicycle with a speed of $12 \; m s^{-1}$ in the east to west direction. What is the direction in which she should hold her umbrella?

Wind is blowing in the north direction at a speed of $2 \, m/s$,which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?

$A$ boy is running on a plane road with velocity $v$ with a long hollow tube in his hand. The water is falling vertically downwards with velocity $u$. At what angle to the vertical,he must incline the tube so that the water drops enter it without touching its sides?