Chapter 5.2, Problem 13E

Reminder Round all answers to two decimal places unless otherwise indicated.

Length of Skid Marks Versus Speed When a car skids to a stop, the length $L$, in feet, of the skid marks is related to the speed $S$, in miles per hour, of the car by the power function $L=\frac{1}{30h}{S}^2$. Here the constant $h$ is the friction coefficient, which depends on the road surface. For dry concrete pavement, the value of $h$ is about $0.85$.

a. If a driver going $55\text{ miles per hour}$ on dry concrete jams on the brakes and skids to a stop. how long will the skid marks be?

b. A policeman investigating an accident on dry concrete pavement finds skid marks $230\text{ feet}$ long. The speed limit in the area is $60\text{ miles per hour}$. Is the driver in danger of getting a speeding ticket?

c This part of the problem applies to any road surface, so the value of $h$ is not known. Suppose you are driving at $60\text{ miles per hour}$, but, because of approaching darkness, you wish to slow to a speed that will cut your emergency stopping distance in half. What should your new speed be?

(Hint: You should use the homogeneity property of power functions here. By what factor should you change your speed to ensure that L changes by a factor of 0.5?)