Question

A car travels due east with a speed of 35.0 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 40.0° with the vertical. Find the velocity of the rain with respect to the following reference frames.

a) car
b) earth

Answer 1

a) They have told you that the rain is falling vertically. Call its vertical velocity Vy. In the reference frame of the car, the rain also has a horizontal component of Vx = 35 km/h and a vertical component Vy. Because of the 40 degree tracks of the drops,
Vx/Vy = tan 40 = 0.839
Vy = 1.19*Vx = 41.7 km/h
Magnitude of velocity = sqrt (Vx^2 + Vy^2) = 54.5 km/h

b) In the earth references frame, the only velocity componenet is the vertical one, Vx, which is the same as in part (a)

Answer 2

56

Answer 3

car: 35km/h divided by tan (40) = 41.7 sqrt of 35^2+41.7^2=54.4
earth: use Pythagorean theorem sqrt 54.4^2-35^2=41.6
use the same 40 degrees in the answer
Unsure if earth is right, but I had 38.0km/h at 62 degrees for my problem and used those steps to get 43.0 km/h for the car and 20.1km/h for Earth. They were correct so here is my input