You are holding a 1 kg rock and standing at the top of a cliff. You drop the rock off the cliff and it falls a distance 10 m. In this problem, you can ignore air resistance.
What is the change in the kinetic energy of the rock as it falls that distance?

98J

Explanation:

Given that the mass of the rock m=1kg, the height =10m and we know that gravitational force is .

Change in kinetic energy  happens when the initial potential energy at rest is converted into Kinetic energy as:

Hence, the change in kinetic energy of the rock is 98J

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 .