One kind of slingshot consists of a pocket that holds a pebble and is whirled on

Question

One kind of slingshot consists of a pocket that holds a pebble and is whirled on a circle of radius r. The pebble is released from the circle at an angle ?, so that it will hit the target. The distance to the target from the center of the circle is d. (See the drawing, which is not to scale.) The circular path is parallel to the ground, and the target lies in the plane of the circle. The distance d is 4.60 times the radius r. Ignore the effects of gravity in pulling the stone downward after it is released and find the angle ?.

Explanation / Answer

as best I can figure out your geometry, the rock is flung in a straight line, tangent to the circle, toward the target

draw a triangle with one side being the line connecting the center of the circle to the target, another line connecting the center of the circle to the rock's launch point, and call the angle between those lines theta

now, since the path of the rock is tangent to the circle, we know that path forms a right angle with the radius line

this means that the line from the center of the circle to the target is the hypotenuse of this triangle, and has length equal to 4.60r

using the figure you drew with the definition provided here for theta, and you can see that

cos(theta)=r/4.60r or cos(theta)=1/4.60

this means that theta = 85.3 deg

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