(Modeling) Grade Resistance See Example 3 to work Exercises 59–65. A 3000-lb car travel...

(Modeling) Grade Resistance See Example 3 to work Exercises 59–65.

A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the nearest tenth of a degree.

(Reference Example 3)

When an automobile travels uphill or downhill on a highway, it experiences a force due to gravity. This force F in pounds is the grade resistance and is modeled by the equation

where u is the grade and W is the weight of the automobile. If the automobile is moving uphill, then < 0°. See Figure 17. (Source: Mannering, F. and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.)

(a) Calculate F to the nearest 10 lb for a 2500-lb car traveling an uphill grade with = 2.5 °.

(b) Calculate F to the nearest 10 lb for a 5000-lb truck traveling a downhill grade with = -6.1°.

(c) Calculate F for = 90°. Do these answers agree with your intuition?