Math

QuestionA car on a 2.62.6^{\circ} incline faces 124lb124 \mathrm{lb} resistance. Find the car's weight to the nearest hundred pounds.

Studdy Solution

STEP 1

Assumptions1. The car is traveling on a .6.6^{\circ} uphill grade. . The grade resistance of the car is 124lb124 \mathrm{lb}.
3. The weight of the car is what we are trying to find.
4. The formula for grade resistance is GR=Wsin(θ)GR = W \cdot \sin(\theta), where GRGR is the grade resistance, WW is the weight of the car, and θ\theta is the grade in degrees.

STEP 2

We need to find the weight of the car, so we rearrange the formula for grade resistance to solve for WW.
W=GRsin(θ)W = \frac{GR}{\sin(\theta)}

STEP 3

Now, plug in the given values for the grade resistance and the grade to calculate the weight.
W=124lbsin(2.6)W = \frac{124 \mathrm{lb}}{\sin(2.6^{\circ})}

STEP 4

First, we need to convert the grade from degrees to radians because the sin\sin function in most calculators uses radians. We can do this by multiplying the grade in degrees by π180\frac{\pi}{180}.
2.6=2.6π180radians2.6^{\circ} =2.6 \cdot \frac{\pi}{180} \, \mathrm{radians}

STEP 5

Now, plug in the converted value for the grade into the formula to calculate the weight.
W=124lbsin(2.π180)W = \frac{124 \mathrm{lb}}{\sin(2. \cdot \frac{\pi}{180})}

STEP 6

Calculate the weight of the car.
W2731lbW \approx2731 \mathrm{lb}

STEP 7

The problem asks for the weight of the car to the nearest hundred pounds. So, we round the calculated weight to the nearest hundred.
W2700lbW \approx2700 \mathrm{lb}The weight of the car is approximately2700 lb.

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