problem 3 You are driving on a highway at night and you noti

problem 3

You are driving on a highway at night and you notice that wheels on the car driving next to you appear stationary. A friend tells you this optical illusion is due to the fact that the sodium discharge lights illuminating the wheel flicker at 55 Hz, so what you see is the same as a video camera operating at a 55Hz framcrate. If the car moves forward 1.2 meters for every rotation of the tire, and the wheels have 4 spokes, then how is the car moving?

Solution

The car moves 1.2 m for every rotation of tire

So, 2*pi*r = 1.2

So, r = 0.6/pi = 0.191 m

frequency of flicker, f = 55 Hz

So, time period, T = 1/f = 1/55 = 0.0182 s

So, after time T, one of spokes cover pi/2 radians

So, time taken to cover 2*pi radians = 4T = 4*0.0182 = 0.0728 s

So, speed of the car = 1.2/0.0728 = 16.5 m/s <-------answer