Final answer:
To determine the weight of the car on an uphill slope, we can use the formula for grade resistance. Applying the formula to the given values, the weight of the car is approximately 5600 lb. The correct answer is option (B).
Step-by-step explanation:
To determine the weight of the car, we need to first understand the concept of grade resistance. Grade resistance is the force that opposes the motion of a car traveling on an incline. In this case, the car is traveling on a 2.7° uphill grade and has a grade resistance of 120 lb.
Grade resistance can be calculated using the formula:
Grade resistance = weight of the car * sin(grade angle)
Rearranging the formula, we can solve for the weight of the car:
Weight of the car = grade resistance / sin(grade angle)
Substituting the values into the formula, we get:
Weight of the car = 120 lb / sin(2.7°) ≈ 5600 lb
Therefore, the weight of the car to the nearest hundred pounds is option B) 5600 lb.