You bicycle along a straight flat road with a safety light attached to one foot.

Question

You bicycle along a straight flat road with a safety light attached to one foot. Your bike moves at a speed of 10 km/hr and your foot moves in a circle of radius 16| cm centered 26|cm above the ground, making one revolution per second. (a) Find parametric equations for x and y which describe the path traced out by the light, where y is distance (in cm) above the ground and x the horizontal distance (in cm) starting position of the center of the circle around which your foot moves. Assuming the light starts 26 cm above the ground, at the front of its rotation. x(t) =, y(t) =. On a separate sheet of paper, sketch the path that your equations describe. (b) How fast (in revolutions/sec) would your foot have to be rotating if an observer standing at the side of the road sees the light moving backward? Rotate at revolutions/second.

Explanation / Answer

y(t) = 0.42 - 0.16 cos ,

x(t) = 10 t - 0.16 sin ;

= 3600 ( 2 ) t ; t in [0,) ,

t is measured in hours , x & y in km/h

NOTE : measured clockwise from the point

( 0 , 26 ) where the foot starts

that is asking when is dx / dt < 0...

dx /dt = 10 - 0.16cos (7200 t ) [ 7200 ]

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