A man is running at a speed of $5\, m/s$, the rain drops appear to be falling at an angle of $45^o$ from the vertical. If the rain drops are actually falling vertically downwards, then velocity of rain drops (in $m/s$) is

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

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

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 ........

The width of river is $1\; km$. The velocity of boat is $5\; km/hr$. The boat covered the width of river with shortest will possible path in $15 \;min$. Then the velocity of river stream is

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...........$km/h$