A man when standstill observes the rain falling vertically and when he walks at `4 km//h` he has to hold his umberella at an angle `53^(@)` from the vertical. Find velocity of the raindrops.

Explanation

Assigning usual symbols `vec(v)_(m), vec(v)_(r)` and `vec(v)_(r//m)` to velocity of man, velocity of rain and velocity of rain relation to man, we can express their relationship by the following eq. `vec(v)_(r)=vec(v)_(m)+vec(v)_(r//m)`
The above equation suggests that a standstill man observes velocity`vec(v)_(r)` of rain relative to the ground and while he is moving with velocity `vec(v)_(m)`, he observes velocity of rain relative to himself `vec(v)_(r//m)`. It is a common intuitive fact that umbrella must be held aganist `vec(v)_(r//m)` for optimum protection from rain. According to these facts, directions of the velocity vectors are shown in the adjoining figure.
The addition of velocity vectors is represented according to the above equation is also represented. From the figure we have
`v_(r)=v_(m) tan 37^(@)=3` km/h