$A$ man is running on a level road with a speed of $10 \ m/s$. He feels that the rain is falling vertically downward with a speed of $10 \sqrt{3} \ m/s$. If he runs in the opposite direction with the same speed,then the speed of the rain relative to him will be:

Particle $A$ (which was located at the origin at time $t=0$) is moving along the $x$-axis with a constant speed of $1 \,m/s$. The location of particle $B$, which is moving along the $y$-axis, is given by $y=ct^2$, where $c=1 \,m/s^2$. Find the speed of particle $A$ relative to particle $B$ at $t=1 \,s$.

Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. $A$ girl is driving a scooty with a speed of $60 \ km/h$ in the direction $X$ to $Y$ and notices that a bus goes past her every $30$ minutes in the direction of her motion,and every $10$ minutes in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.

$A$ person is swimming with a speed of $10\, m/s$ at an angle of $120^{\circ}$ with the flow of the river and reaches a point directly opposite on the other side. If the speed of the river flow is $x\, m/s$,find the value of $x$ to the nearest integer.

Two girls are standing at the ends $A$ and $B$ of a ground where $AB = b$. The girl at $B$ starts running in a direction perpendicular to $AB$ with velocity $V_1$. The girl at $A$ starts running simultaneously with velocity $V_2$ and meets the other girl in the shortest possible time $t$. The value of $t$ is:

Two cars $A$ and $B$ are moving with a velocity of $30 \ km/h$ in the same direction. They are separated by $10 \ km$. The speed of another car $C$ moving in the opposite direction,if it meets these two cars at an interval of $8 \ minutes$,is: (in $km/h$)