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 34.2°. 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 eleven times the radius r. Ignore the effect of gravity in pulling the stone downward after it is released and find the angle .

Explanation / Answer

Here ,

as the pebble will move tangential to the circle

after firing from the slingshot

phi = 34.2 degree

angle between radius and distance d vectror

as radius is perpendicular to the tangent

angle= arccos(r/11r)

angle = 84.8 degree

Now , for angle theta

angle + theta + phi = 180

84.8 + 34.2 + theta = 180

solving for theta

theta = 61 degree

the angle theta must be 61 degree

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