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January 29, 2015

January 29, 2015

Posted by **sophie** on Sunday, May 22, 2011 at 12:16am.

At what rate is the shadow moving when it is 15 ft from the point on the wall that is closest to the merry-go-round?

- math -
**drwls**, Sunday, May 22, 2011 at 9:37amDraw a figure with a circle of radius 25 and a flat sceen behind it. Draw a line through the center of the circle that extends back to the screen, which will be perpendicular to the line. Let the angle of Kelly's location from the sun direction line be A.

A = sin^-1 15/25 = 36.8 degrees

The location of the shadow relative to the closest position (where the line meets the wall) is

X = R sin A

The rate the shadow moves is

dX/dt = R cos A* dA/dt

where dA/dt is in radians/s

dA/dt = (2 pi/10 rad)/1 s

= 0.6283 rad/s

dX/dt = 25 ft*0.8*0.6283 rad/s= 12.6 ft/s

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