Merry-go-round. two identical twins, jena and jackie, are playing one december on a large merry-go-round (a disk mounted parallel to the ground on a vertical axle through its center) in their school playground in northern minnesota. each twin has a mass of 29.0 kg. the icy coating on the merry-go-round surface makes it frictionless. the merry-go-round revolves at a constant rate as the twins ride on it. jena, sitting a distance 1.71m from the center of the merry-go-round, must hold on to one of the metal posts attached to the merry-go-round with a horizontal force of 56.0 n to keep from sliding off. jackie is sitting at the edge, a distance 3.58 m from the center. with what horizontal force must jackie hold on to keep from falling off?

245.44 N

Explanation:

Given

mass of each twins(m)=29 kg

Jena distance from center is 1.71 m

Horizontal force applied is 56 N

Jackie distance from center is 3.58

centripetal force is given by

In first case horizontal force is balanced by Centrifugal force

----1

----2

Divide 1 & 2 we get

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

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