Answer to Question #3863 in Mechanics | Relativity for mia

Question

The driver notices that the rain leaves no trace on the back windshield of his car slanted at a 60° angle to the horizontal when the car is moving faster than 30 km per hour. Find the velocity of rain droplets.

Answer 1

Let V be the vector of velocity of rain droplets directed downwards, U - vector of
velocity of the car.
If we consider the car as a moving system of coordinates, then the velocity of the rain will be the sum of 2 perpendicular vectors: U+V.
As the droplets leave no trace on the back windshield of the car, the resulting vector is parallel to the windshield.
So tan(60°)=|V|/|U|.


Then |V|=tan(60°)*|U| = sqrt(3)*30 = 52 km/h.


So, the velocity of rain droplets is 52 km per hour.