A person running horizontally observes that rain is falling on his head vertically with speed $10\,m/s$. He stops and observes that rain is coming at an angle $30^o$ with vertical., find the speed with which man was running

Figure shows two ships moving in $x-y$ plane with velocities $V_A$ and $V_B$. The ships move such that $B$ always remains north of $A$. The ratio $\frac{V_A}{V_B}$ is equal to ........

An aeroplane is to go along straight line from $A$ to $B$, and back again. The relative speed with respect to wind is $V$. The wind blows perpendicular to line $AB$ with speed $v$. The distance between $A$ and $B$ is $\ell $. The total time for the round trip is

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$......$

A boat crosses a river with a velocity of $8\, km/h$. If the resulting velocity of boat is $10 \,km/h $ then the velocity of river water is...........$km/h$

A boat takes two hours to travel $8 \,km$ and back in still water. If the velocity of water is $4\, km/h$, the time taken for going upstream $8 \,km$ and coming back is