A car travels due east with a speed of 52.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 66.0° with the vertical. Find the velocity of the rain with respect to the following reference frames. (Enter the magnitude of the velocity.)

(a) the car

m/s

(b) the Earth

m/s

a) v = 6.43 m/s

b) v = 15.8 m/s

Explanation:

Speed of car = 56 km/h

56 km/h = 14.4 m/s

Angle rain makes on the glass to the vertical = 66°

Thus knowing that the opposite side of the angle is the distance moved by the car, and the adjacent side is the distance traveled by the rain in the same time

both of which are directly proportional to their velocities

Then

tan (66°) = 14.44m/s : x

or x = 14.44/tan (66°)

Which is the vertical raindrop velocity of the relative to earth

v = 6.43 m/s vertically towards earth

For v relative to the car is we have vector sum of both velocities

v = √ (14.44^2 + 6.43^2) = 15.8 m/s which is the velocity relative to car

= 15.8 m/s