Chapter 9.5, Problem 42PPS

To determine

The speed limit on highway is 65 mph, find her speed and check she is speeding or not?

Answer to Problem 42PPS

No, she was not speeding.

Explanation of Solution

Given:

The equation $d=0.05v^2+1.1v$ models the distance d in feet it takes a car travelling at a speed of v miles per hour to come to a complete stop. The speed limit on some highways is 65 miles per hour. If Hannah`s car stopped after 250 feet, was she speeding? Explain your reasoning.

Concept Used:

Hannah`s car stopped after 250 feet, this means d = 250

The required equation: $250=0.05v^2+1.1v$

Calculation:

Write the equation in Standard Form:

  $\begin{array}{l}250=0.05v^2+1.1v\\ 0=0.05v^2+1.1v-250\\ 0.05v^2+1.1v-250=0\end{array}$

Use Quadratic formula to solve the equation:

For this equation: $0.05v^2+1.1v-250=0\Rightarrow a=0.05,b=1.1,\text{and}c=-250$

Quadratic Formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

  $\begin{array}{l}x=\frac{-1.1\pm \sqrt{{(1.1)}^2-4·(0.05)·(-250})}{2·(0.05)}=\frac{-1.1\pm \sqrt{1.21+50}}{0.1}=\frac{-1.1\pm \sqrt{51.21}}{0.1}\\ x=\frac{-1.1+\sqrt{51.21}}{0.1}\text{or}x=\frac{-1.1-\sqrt{51.21}}{0.1}\\ x\approx 61\text{or}x\approx -83\end{array}$

No, she was not speeding, as Hannah was travelling at about 61 mph, so she was not speeding.

Thus, no, she was not speeding.