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.

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.
Transcript text: 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 $\theta$ is the grade and $W$ is the weight of the automobile. \[ F=W \sin \theta \] What is the grade resistance of a 2000-pound car traveling on a $1.7^{\circ}$ uphill grade? The grade resistance is $\square$ pounds.
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Solution

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Solution Steps

Step 1: Identify the Given Values

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

Step 2: Use the Grade Resistance Formula

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

Step 3: Calculate the Sine of the Angle

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

Step 4: Calculate the Grade Resistance

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

Final Answer

The grade resistance of the car is \(\boxed{59.4}\) pounds.

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