$A$ 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:

If the velocities of object $A$ and $B$ are $v_A$ and $v_B$ respectively,then write the equation of the relative velocity of $A$ with respect to $B$.

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

When a car is at rest,its driver sees rain drops falling on it vertically. When driving the car with speed $v$,he sees that rain drops are coming at an angle $60^{\circ}$ from the horizontal. On further increasing the speed of the car to $(1+\beta)v$,this angle changes to $45^{\circ}$. The value of $\beta$ is close to...

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.

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: