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.