By the term velocity of rain, we mean velocity with which raindrops fall relative to the ground. In absence of wind, raindrops fall vertically and in presence of wind raindrops fall obliqucly. Moreover raindrops acquire a constant terminal velocity due air resistance very quickly as they fall toward the carth. A moving man relative to himself observes an altered velocity of raindrops. Which is known as velocity of rain relative to the man. It is given by the following equation.
`vec(v)_(rm)=vec(v)_(r)-vec(v)_(m)`
A standstill man relative to himself observes rain falling with velocity, which is equal to velocity of the raindrops relative to the ground. To protect himself a man should his umbrella against velocity of raindrops relative to himself as shown in the following figure.

When you walk in rain at 75 cm/s, you have to hold your umbrella vertically and when you double your speed in the same direction, you have to hold your unbrella at `53^(@)` above the horizontal. what is the rain velocity ?

Answer

125 cm/s at `37^(@)` from the vertical