One type of slingshot can be made from a length of rope and a leather pocket for

Question

One type of slingshot can be made from a length of rope and a leather pocket for holding the stone. The stone can be thrown by whirling it rapidly in a horizontal circle and releasing it at the right moment. Such a slingshot is used to throw a stone from the edge of a cliff, the point of release being 27.5 m above the base of the cliff. The stone lands on the ground below the cliff at a point X. The horizontal distance of point X from the base of the cliff (directly beneath the point of release) is 34.7 times the radius of the circle on which the stone is whirled. Determine the angular speed of the stone at the moment of release.

Explanation / Answer

as stone is relleased horizontally, (that means it have no initial vertical velocity , uy = 0 )

as it goes 27.5 m vertically downwrads.

using y = uy*t + ay*t^2 /2

-27.5 = 0 - 9.81 t^2 /2

t = 2.37 sec

In this time horizontal distance traveled   = vt = 34.7R

so v = 34.7R / 2.37 = 14.65R

angular speed w = v /R = (14.65R/R) =14.65 rad/s ........Ans

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