A person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of $0.5\, m/s$ at an angle of $120^°$ with the direction of flow of water. The speed of water in the stream is..........$m/s$

$A$ ship $X$ moving due north with speed $v$ observes that another ship $Y$ is moving due west with same speed $v$. The actual velocity of $Y$ is $........$.

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.

A man standing on a road hold his umbrella at $30^° $ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\, km/hr$. He finds that raindrops are hitting his head vertically, the speed of raindrops w.r.t. the moving man, will be

Thief's car is moving with a speed of $10\,m/s$. A police van chasing this car with a speed of $5\,m/s$ fires a bullet at the thief's car with muzzle velocity $72\,km/h$. Find the speed with which the bullet with hit the car.............$m/s$

When a train is at rest, rain drops fall vertically. When it moves along east with a velocity equal to that of rain, the rain will appear to fall, for a passenger in the train