What Is the Speed and Angle of Raindrops in Different Reference Frames?

[RockenNS42]

Homework Statement

While driving north at 25 during a rainstorm you notice that the rain makes an angle of 38 with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down.
a)From these observations, determine the speed of the raindrops relative to the ground.
b)From these observations, determine the angle of the raindrops relative to the ground.

Homework Equations

V=v_y+v_x
V^'=V_R-V

Where V_R is the velocity of the rain

The Attempt at a Solution

When driving north I got

V=(-v_Rsinθ_R)i + (-v_Rcosθ_R)j

Using

V^'=V_R-V

I get V^'=V_R-V(-v_Rsinθ_R-25)i + (-v_Rcosθ_R)j




Im not sure how to set it up for going south. Any suggestions?
Would it look like this? V^'=0i+ (-v_Rcosθ_R)j
?
And to find θ, would i use [ v^'_x / v^'_y}tan_-1?


I thinks mostly all the subscripts and whatnot that's messing me up.
Thanks in advance for any help given :)

 

[Spinnor]

Think of the three reference frames in this problem of interest. At rest relative to earth, moving away from home in the car, moving towards home in the car. In each reference frame the rain will be falling at a different angle. See,



Good luck!