Chapter 8.5, Problem 48PPS

a.

To determine

To write: The expression of height in factored form.

Answer to Problem 48PPS

  $-16\left(t^2+6t-10\right)$

Explanation of Solution

Given:

The height of a rider in feet t seconds after being dropped on a drop tower thrill can be modeled as $-16t^2-96t+160$

Calculation:

The given expression is $-16t^2-96t+160$

Factored out the GCF

  $-16\left(t^2+6t-10\right)$

This polynomial is a prime polynomial. Hence, it cannot be further factored.

Therefore, the expression of the height can be written in factored form as $-16\left(t^2+6t-10\right)$

b.

To determine

To find: The height from which the rider initially dropped.

Answer to Problem 48PPS

160 feet.

Explanation of Solution

Given:

The height of a rider in feet t seconds after being dropped on a drop tower thrill can be modeled as $-16t^2-96t+160$

Calculation:

When the rider is initially dropped, the time will be zero.

Hence, substituting $t=0$ in the given expression

  $\begin{array}{l}-16{\left(0\right)}^2-96\left(0\right)+160\\ =160\end{array}$

Therefore, the rider was initially dropped from a height of 160 feet.

c.

To determine

To find: The height will the rider be after 3 seconds of falling. Is this possible? Explain the reasoning.

Answer to Problem 48PPS

  $-272\text{ feet}$

Explanation of Solution

Given:

The height of a rider in feet t seconds after being dropped on a drop tower thrill can be modeled as $-16t^2-96t+160$

Calculation:

Hence, substituting $t=3$ in the given expression

  $\begin{array}{l}-16{\left(3\right)}^2-96\left(3\right)+160\\ =-144-288+160\\ =-272\end{array}$

The height cannot be negative. Hence, it is not possible.