Vector problems?

Question

This is a problem of mine for physics:

A car travels due east with a speed of 50.0 km/h. Rain is falling vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 50.0° with the vertical. Find the velocity of the rain with respect to each of the following.

a) The car(in m/s)
b) The Earth (in m/s)

I've been attempting these for a while. The only solution I could come up with for A is Tan50=x/13.9. I got the answer then converted from km/h to m/s to get 16.56. The computer is telling me this is wrong. I have no idea what to do next.

Any help or guidance would be great on both! Thanks!

Answer 1

Hi Countrygurl....

With respect to the car, the rain has two vector components. Vx = Car's velocity = 50 klicks/hr=50,000m/3600sec=13.9m/s
and
Vy = Downward velocity
We also know the angle which is 50deg off of verticle,

Solve for b (Vy) first:

Tan (50) = Vx/Vy=13.9m/s*1/Vy.
Vy=13.9/Tan(50)
=11.65 m/s

Now solve for Velocity with respect to car

=Sqrt(Vx^2 + Vy^2)
=Sqrt(13.9^2+11.65^2)
=18.14 m/sec

Note: It looks like you were on the right track before you asked for help.