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 phi in the drawing is 32.8. 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 four times the radius r. Ignore the effect of gravity in pulling the stone downward after it is released and find the angle ?.

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 phi in the drawing is 32.8½. 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 four times the radius r. Ignore the effect of gravity in pulling the stone downward after it is released and find the angle ?.

Explanation / Answer

I think you are looking for the size of angle theta. I assume it is the angle between the line joining the center of the circle, O, and the target, T, with the line from the center of the circle to the release point, P. The stone leaves the circle on a tangent, so the line of flight is perpendicular to the radius. Then OPT is a right triangle with the right angle at P. The radius has length 1, and the distance is 10. Therefore the angle, theta, is determined by cos (theta) = 1/10 I don't know where your 35 degrees comes into the diagram.

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