Questions: When an automobile travels uphill or downhill on a highway, it experiences a force due to gravity. This force in pounds is called grade resistance and is modeled by the following equation, where θ is the grade and W is the weight of the automobile. F=W sin θ What is the grade resistance of a 2000-pound car traveling on a 1.7° uphill grade? The grade resistance is pounds.

Solution Steps

We are given the weight of the car, $W = 2000$ pounds, and the angle of the uphill grade, $\theta = 1.7^\circ$.

The formula for grade resistance is given by: $$F = W \sin \theta$$ Substitute the given values into the formula: $$F = 2000 \sin(1.7^\circ)$$

Calculate $\sin(1.7^\circ)$ using a calculator: $$\sin(1.7^\circ) \approx 0.0297$$

Substitute $\sin(1.7^\circ)$ into the formula: $$F = 2000 \times 0.0297 = 59.4$$

Final Answer