On a stormy day you are sitting in the driver’s seat in your car, stopped at a s

Question

On a stormy day you are sitting in the driver’s seat in your car, stopped at a stoplight, and looking out the driver’s side window. You notice that the rain hitting your window is sliding down the glass at roughly 20 from the vertical, towards the back of the car. The stoplight turns green, and you quickly accelerate your car to a constant speed of 45 mph. Once you’re at that constant speed you look out your window again. The rain is now hitting your window at roughly 70 from vertical towards the back of the car. From these observations, calculate the speed at which the rain is falling.

Explanation / Answer

velocity of rain relative to ground vrg = v*sin20i - v*cos20 j

velocity of car reatie to ground vcg = -45 i

velocity of rain relative to car vrc = vrg + vgc = vrg - vcg

vrc = (v*sin20 + 45)i - v*cos20 j

angle made by vrc with the vertical = tan^-1((v*sin20 + 45)/vcos20) = 70

v = 17.4 mph <<<<---------ANSWER

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