Chapter 8.1, Problem 46PPSE

Solution

To find: the maximum height that the ball reaches.

Maximum height is 144ft. Option C is correct.

Given information:

The quadratic equation for height is:

  $h\left(t\right)=-16t^2+96t$

Concept:

To find the time at which the ball attains maximum height, differentiate the given quadratic equation and then equate that with zero.

Then put the value in the equation to determine the maximum height.

Calculation:

  $\begin{array}{c}h\left(t\right)=-16t^2+96t\\ h\text{'}\left(t\right)=2\left(-16t\right)+96\\ h\text{'}\left(t\right)=-32t+96\\ 0=-32t+96\\ 32t=96\\ t=3\end{array}$

Now put the value of time in the equation to find the maximum height,

  $\begin{array}{l}h\left(3\right)=-16\left(3^2\right)+96\left(3\right)\\ h\left(3\right)=144ft\end{array}$

Conclusion:

Hence, the maximum height is 144ft.