Question

Airplane height, in feet: h = 144Baseball height, in feet: h = 96t - 1612Choose the graph of the system shown above.

Answer 1

Given:

The airplane height

`h=144`

Baseball height is

`h=96t-16t^2`

Find-:

Chose the function graph

Explanation-:

The maximum value of baseball height is

`h=96t-16t^2`

The critical value is

`\begin{gathered} h=96t-16t^2 \\ \\ h^(\prime)=96-16(2)t \\ \\ h^(\prime)=96-32t \end{gathered}`

For the maximum value is h' = 0 is

`\begin{gathered} h^(\prime)=0 \\ \\ 96-32t=0 \\ \\ 32t=96 \\ \\ t=(96)/(32) \\ \\ t=3 \end{gathered}`

The maximum value at " t = 3 "

`\begin{gathered} h=96t-16t^2 \\ \\ t=3 \\ \\ h=96(3)-16(3^2) \\ \\ h=96(3)-16(9) \\ \\ h=288-144 \\ \\ h=144 \end{gathered}`

The t² is a negative value so the graph is down open graph

Then the graph is

So, option "C" is the right choose.