A0.537-kg basketball is dropped out of a window that is 5.88 m above the ground. the ball is caught by a person whose hands are 1.98m above the ground. (a) how much work is done on the ball by its weight? what is the gravitational potential energy of the basketball, relative to the ground, when it is (b) released and (c) caught? (d) what is the change () in the ball's gravitational potential energy?

a) 20.54 J

b) 30.97 J

c) 10.43 J

d) -20.54 J

Explanation:

m = Mass

g = Acceleration due to gravity = 9.81 m/s²

h = Height

Work done by the ball's weight is 20.54 J

Gravitational potential energy of the basketball, relative to the ground, when it is released is 30.97 J

Gravitational potential energy of the basketball, relative to the ground, when it is released is 10.43 J

Change in gravitational potential energy

Change in gravitational potential energy is given by -20.54 J

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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 .