Question

a car traveling on a 1.9° uphill grade has a grade resistance of 114 lb. determine the weight of the car to the nearest hundred pounds. the weight of the car is approximately lb.

Explanation:

Step1: Recall grade - resistance formula

The grade - resistance $F$ is given by the formula $F = W\sin\theta$, where $W$ is the weight of the vehicle and $\theta$ is the angle of the grade. We need to solve for $W$.

Step2: Rearrange the formula for $W$

From $F = W\sin\theta$, we can solve for $W$ by dividing both sides of the equation by $\sin\theta$. So, $W=\frac{F}{\sin\theta}$.

Step3: Substitute the given values

We are given that $F = 114$ lb and $\theta=1.9^{\circ}$. First, find $\sin(1.9^{\circ})$. Using a calculator, $\sin(1.9^{\circ})\approx0.0331$. Then, $W=\frac{114}{0.0331}\approx3444$ lb.

Step4: Round to the nearest hundred pounds

Rounding 3444 lb to the nearest hundred pounds, we get 3400 lb.

Answer:

3400