$A$ flag is mounted on a car moving due North with a velocity of $20 \, km/hr$. Strong winds are blowing due East with a velocity of $20 \, km/hr$. The flag will point in which direction?

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?

Particle $A$ moves along the $X$-axis with a uniform velocity of magnitude $10 \ m/s$. Particle $B$ moves with a uniform velocity of $20 \ m/s$ along a direction making an angle of $60^{\circ}$ with the positive direction of the $X$-axis as shown in the figure. The relative velocity of $B$ with respect to $A$ is

$A$ person running horizontally observes that rain is falling on his head vertically with a speed of $10\,m/s$. When he stops,he observes that the rain is falling at an angle of $30^o$ with the vertical. Find the speed with which the man was running.

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 $\text{ km/h}$)?

Match Column-$I$ with Column-$II$ correctly.

Column-$I$	Column-$II$
$(1)$ Velocity of $A$ relative to $B$ if $A$ and $B$ are moving perpendicular to each other	$(a)$ $\vec{v}_{rm} = \vec{v}_r + \vec{v}_m$
$(2)$ Velocity of rain drops relative to a man	$(b)$ $\vec{v}_{AB} = \vec{v}_A + \vec{v}_B$
	$(c)$ $v_{AB} = \sqrt{v_A^2 + v_B^2}$