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 the angle so that it will hit the target. The angle in the drawing is 32.0°. The distance to the target from the center of the circle is d. (See the drawing below, 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 one times the radius r. Ignore the effect of gravity in pulling the stone downward after it is released and find the angle .
  °

Explanation / Answer

r and d may both be measured from the center of the circle.
If r is exactly the same as d then the pebble should be released when the string lies on angle

= 180 -
= 180 - 32
= 148°

If d is measured from the circle circumference, then the total distance from C to the target is 2r
the pebble should be released when the string is perpendicular to the tangent from the circle to the target.
As the near leg of a right triangle will be half of the hypotenuse, the internal angle will be 60° so

= 180 - 32 - 60
= 88°

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