Chapter 8.3, Problem 27E

a.

To determine

To find the time when the firework explodes.

Answer to Problem 27E

The firework will explode after $4$ seconds.

Explanation of Solution

Given:

The following function shows height $h$ of a firework after $t$ seconds.

  $h=-16t^2+128t$

Calculation:

The firework will explode at the maximum point of the parabola which in this case is vertex.

So,

  $\begin{array}{l}t=-\frac{b}{2a}\\ t=-\frac{128}{2(-16)}\\ t=4\end{array}$

Hence, the firework will explode after $4$ seconds.

b.

To determine

To find the height at which the firework will explode.

Answer to Problem 27E

The firework will explode at $256\text{ feet}$ from ground.

Explanation of Solution

Given:

The following function shows height $h$ of a firework after $t$ seconds.

  $h=-16t^2+128t$

Calculation:

Substitute $t=4$ to find the value of $h$

  $\begin{array}{l}h=-16t^2+128t\\ h=-16\times 4^2+128\times 4\\ h=-256+512\\ h=256\text{ feet}\end{array}$

Therefore the firework will explode at $256\text{ feet}$ from ground.