Chapter 8.5, Problem 74ES

The functions

$f(x)=0.0875x^2-0.4x+66.6$

Dry pavement

and

Wet pavement

$g(x)=0.0875x^2+1.9x+11.6$

model a car’s stopping distance, $f(x)$ or $g(x)$, in feet, traveling at $x$ miles per hour. Function $f$ models stopping distance on dry pavement and function $g$ models stopping distance on wet pavement. The graphs of these functions are shown for speed of 30 miles per hour and greater. Notice that the figure does not specify which graph is the model for dry roads and which is the model for wet roads. Use this information to solve Exercises 73

a Use the given functions to find the stopping distance on dry pavement and the stopping distance on wet pavement for a car traveling at 55 miles per hour. Round to the nearest foot.

b. Based on your answers to part (a), which rectangular coordinate graph shows stopping distances on dry pavement and which shows stopping distances on wet pavement?

c. How well do your answers to part (a) model the actual stopping distances shown in Figure 8.15 on page

d. Determine speeds on wet pavement requiring stopping distances that exceed the length of one and one-half football field, or 540 feet. Round to the nearest mile per hour. How is this shown on the appropriate graph of the models on page