If a brick falls from a building 23.0 meters tall, how much time does it take for it to hit the ground?

It will take t = 2.16 [s]

Explanation:

In order to solve this problem, we must find the final speed of the object when it is on the floor. The only way is to use the principle of energy conservation which tells us that potential energy can be transformed into kinetic energy and vice versa.

Now we can find the velocity

v² = 2*g*h

v = √2*9.81*23

v = 21.24 [m/s]

Now using the following equation:

where:

Vf = final velocity = 21.24 [m/s]

Vo = initial velocity = 0

g = gravity acceleration = 9.81 [m/s²]

t = time [s]

21.24 = 0 + (9.81*t)

t = 2.16 [s]

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 .

the maxium height is 34m/s