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 ..............

A boat is moving with velocity of $3\hat i + 4\hat j$ in river and water is moving with a velocity of $ - 3\hat i - 4\hat j$ with respect to ground. Relative velocity of boat with respect to water is :

A man sitting in a bus travelling in a direction from west to east with a speed of $40 \,km/h $observes that the rain-drops are falling vertically down. To the another man standing on ground the rain will appear

A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of $2\,\,m/s$. At what angle $\alpha$ with the vertical should the wind screen be placed so that the rain drops falling vertically downwards with velocity $6\,\, m/s$ strike the wind screen perpendicularly.

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

A bus appears to go with a speed of $25 \,km / hr$ to a car driver, driving at the rate $7 \,km / hr$ northwards. If the bus actually travels in east direction, its speed is ......... $km / h$