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.
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.