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An interesting application of the relative motion equations is the experimental determination of the speed at which rain falls. Say you perform an experiment in your car in which you park your car in the rain and measure the angle the falling rain makes on your side window. Let this angle be theta rest = 20 degree. Next you drive forward at 25 mph and measure the new angle theta motion = 70 degree that the rain makes with the vertical. Determine the speed of the falling rain.

Explanation / Answer

Lets assmue magnitude of velocity of rain is V

V = - vsin(20) i - v cos(20 deg) j

Relative to car moving at Vc = 25 mph

Vr = - v sin(20) - 25 i - v cos(20) j

given angle is 70 degrees

implies

(v(sin(20) + 25)/(V (cos(20))) = tan(70 deg) = cos(20)/ sin(20)

25 = v cos(40)/(cos(20)*sin(20))

v = 25*tan(40 deg)/2

Speed = 10.49 Mph

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