Question

A person standing close to the edge on the top of a 400-ft building drops a baseball. The quadratic function h left parenthesis t right parenthesis equals negative 16 t squared plus 400 models the ball’s height above the ground, h left parenthesis t right parenthesis, in feet, t seconds after it was dropped.

Find h left parenthesis 0 right parenthesis AND interpret the meaning of the function value in the context of the problem.

Answer 1

`h(0)=400`

The above function value for
`h(0)` shows that height of the ball before it was dropped i.e. at time = 0 seconds.

The height of the ball above the ground before it was dropped = 400 ft.

Explanation:

Given:

The quadratic function that models the height of the baseball above the ground in feet ,
`t` seconds after it was dropped is given as:

`h(t)=-16t^2+400`

To find
`h(0)` and interpret the meaning of the function value in contect of the problem.

Solution:

In order to find
`h(0)`, we will replace
`t=0` in the given function as
`h(t)` is a function of time
`t`.

Thus, we have:

`h(0)=-16(0)^2+400`

`h(0)=16(0)+400`

`h(0)=0+400`

`h(0)=400` (Answer)

The above function value for
`h(0)` shows that height of the ball before it was dropped i.e. at time = 0 seconds.

The height of the ball above the ground before it was dropped = 400 ft.