(Modeling) Car’s Speed at Collision Refer to Exercise 73. An automobile is...

(Modeling) Car’s Speed at Collision Refer to Exercise 73. An automobile is traveling at 90 mph on a highway with a downhill grade of θ = -3.5°. The driver sees a stalled truck in the road 200 ft away and immediately applies the brakes. Assuming that a collision cannot be avoided, how fast (in miles per hour) is the car traveling when it hits the truck? (Use the same values for K1 and K2 as in Exercise 73.)

(Reference Exercise 73)

(Modeling) Braking Distance If aerodynamic resistance is ignored, the braking distance D (in feet) for an automobile to change its velocity from V₁ to V₂ (feet per second) can be modeled using the following equation.

K1 is a constant determined by the efficiency of the brakes and tires, K₂ is a constant determined by the rolling resistance of the automobile, and θ is the grade of the highway. (Source: Mannering, F. and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.)

(a) Compute the number of feet required to slow a car from 55 mph to 30 mph while traveling uphill with a grade of θ = 3.5°. Let K₁ = 0.4 and K₂ = 0.02. (Hint: Change miles per hour to feet per second.)

(b) Repeat part (a) with θ = -2°.

c) How is braking distance affected by grade θ? Does this agree with your driving experience?