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 θ so that it will hit the target. The angle ϕ in the drawing is 37.1°. 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 θ.

Answer 1

Answer:

θ=142.9°

Explanation:

d=1 *r

angle ϕ= 37.1°

the line connecting pebble and target should be tangent to a circle so

cos(180-ϕ-θ)=$\frac{r}{d}$=$\frac{1}{1}$

∴ θ=180-ϕ-$cos^{-1} (\frac{1}{1} )$

  θ= 180-37.1-0

  θ=142.9°