1. Financial Algebra © Cengage/South-Western Slide 1 AUTOMOBILE OWNERSHIP 5-1Classified Ads 5-2Buy or Sell a Car 5-3Graph Frequency Distributions 5-4Automobile Insurance 5-5Linear Automobile Depreciation 5

2. Financial Algebra © Cengage/South-Western Slide 2 AUTOMOBILE OWNERSHIP 5-6Historical and Exponential Depreciation 5-7Driving Data 5-8Driving Safety Data 5-9Accident Investigation Data 5

3. Financial Algebra © Cengage/South-Western Slide 3 5-9 ACCIDENT INVESTIGATION DATA Determine the minimum skid speed using the skid mark formula. Determine the minimum skid speed using the yaw mark formula. OBJECTIVES

4. Financial Algebra © Cengage Learning/South-Western Slide 4 accident reconstructionist skid mark shadow skid mark anti-lock braking system (ABS) yaw mark skid speed formula drag factor braking efficiency skid distance chord middle ordinate Key Terms

5. Financial Algebra © Cengage Learning/South-Western Slide 5 What data might a car leave behind at the scene of an accident? What information might skid marks give an accident reconstructionist?

6. Financial Algebra © Cengage Learning/South-Western Slide 6 Example 1 A car is traveling on an asphalt road with a drag factor 0.78. The speed limit on this portion of the road is 35 mph. The driver just had his car in the shop and his mechanic informed him that the brakes were operating at 100% efficiency. The driver must make an emergency stop, when he sees an obstruction in the road ahead of him. His car leaves four distinct skid marks each 80 feet in length. Q: What is the minimum speed the car was traveling when it entered the skid? Round your answer to the nearest tenth. Q: Was the driver exceeding the speed limit when entering the skid?

7. Financial Algebra © Cengage Learning/South-Western Slide 7 Example 1 Drag factor = 0.78. Speed limit = 35 mph. Skid marks = 80 feet Braking efficiency = 100% or 1.00 Q: What is the minimum speed the car was traveling when it entered the skid? Round your answer to the nearest tenth. Q: Was the driver exceeding the speed limit when entering the skid? S = √30Dfn D = 80; f = 0.78; n = 1.0 S = √30*80*0.78*1.0 = √1872 = 43.3 mph 43.3 > 35; Yes.

8. Financial Algebra © Cengage Learning/South-Western Slide 8 A portion of road has a drag factor of x. A car with a y percent braking efficiency is approaching a traffic jam ahead, causing the driver to apply the brakes for an immediate stop. The car leaves four distinct skid marks of z feet each. Write an expression for determining the minimum speed of the car when entering into the skid. CHECK YOUR UNDERSTANDING

9. Financial Algebra © Cengage Learning/South-Western Slide 9 Average skid distance #2 #3 Skid Speed Formula: #5 #7 Applications, p. 279

10. Financial Algebra © Cengage Learning/South-Western Slide 10 Example 2 Melissa was traveling at 50 mph on a concrete road with a drag factor of 1.2. Her brakes were working at 90% efficiency. To the nearest tenth of a foot, what would you expect the average length of the skid marks to be if she applied her brakes in order to come to an immediate stop? S = √30Dfn S = 50; f = 1.2; n = 0.9 50 = √30*D*1.2*0.9 50 = √32.4D

11. Financial Algebra © Cengage Learning/South-Western Slide 11 Example 2 S = √30Dfn S = 50; f = 1.2; n = 0.9 50 = √30*D*1.2*0.9 50 = √32.4D (50) 2 = (√32.4D) 2 2500 = 32.4D 2500 ÷ 32.4 = D D = 77.2 feet

12. Financial Algebra © Cengage Learning/South-Western Slide 12 #9 #10 #11 Applications, p. 280

13. Financial Algebra © Cengage Learning/South-Western Slide 13 When a vehicle is slipping sideways while at the same time continuing in a forward motion, the marks left on the road surface are curved. Define: Yaw Marks

14. Financial Algebra © Cengage Learning/South-Western Slide 14 EXAMPLE 3 An accident reconstructionist took measurements from yaw marks left at a scene. Using a 43-foot length chord, she determined that the middle ordinate measured approximately 4 feet. The drag factor for the road surface was determined to be 0.8. Determine the radius of the curved yaw mark to the nearest tenth of a foot. Determine the minimum speed that the car was going when the skid occurred to the nearest tenth.

15. Financial Algebra © Cengage Learning/South-Western Slide 15 Determine the minimum speed of a car at the point the brakes are immediately applied to avoid a collision based upon a yaw mark chord measuring 62.4 feet and a middle ordinate measuring 5 feet. The drag factor of the road surface is 1.2. Round your answer to the nearest tenth. CHECK YOUR UNDERSTANDING