As its a homework exercise I  can not do justice- but I can   just point out that at certain velocity ratio  the rain drops will start moving up the wind shield.

One can take the car as stationary and add a  car's velocity vector **V** to rain drops vertically down velocity  **v**- the resultant will be inclined to the vertical say at an angle  $\theta$  and if it has some component sliding along the inclined wind shield it can happen(the droplets will slide up).

When we run on a rainy day(rain falling vertically downward) with an umbrella -the umbrella has to be tilted from the vertical to save us from rain drops and as we speed up  this tilt angle has to be increased.