Review Conceptual Example 2 as background for this problem. One kind of slingsho

Question

Review Conceptual Example 2 as background for this problem. 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 6.24 times the radius r. Ignore the effects of gravity in pulling the stone downward after it is released and find the angle ?.

Review Conceptual Example 2 as background for this problem. 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 theta, 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 6.24 times the radius r. Ignore the effects of gravity in pulling the stone downward after it is released and find the angle theta. Number Units the tolerance is +/-2%

Explanation / Answer

This is a simple geometry problem

pebble will hit the target only if pebble, target and center of circle makes a right angle

so,

r/d = cosx

where x is angle between 35 and theta

r/6.24r = cosx

x = 80.79 deg

Now,

x + 35 + theta = 180

theta = 64.21 deg

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