is the light source between the center of the circle and the object's line, or on the far side of the line? That will affect where the shadow falls.
Also, you have not indicated the speed of the object, dx/dt.
In either case, label the light source L, the object P and the center of the circle O. Let the shadow fall on the circle at point S. You want to figure angle LOS = LOP = θ.
Once you have figured dθ/dt in terms of dx/dt (when x=1), then the speed along the circle can be found using
s = rθ
ds/dt = r dθ/dt
) An object is moving on a straight line which is 15 centimeters away from the center of a circle of radius 28 centimeters. (Both the circle and the straight line are on the same plane.) A source of light is located on the line drawn from the center of the circle perpendicular to the original line, and is 10 centimeters away from the original line. What is the speed of the shadow of the moving object (projected on the circle) when the object is one centimeter away from the intersection of the two lines?
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1 answer