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

Answer:

$h(0)=400$

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.

Step-by-step 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.