(Modeling) Grade Resistance Solve each problem. See Example 3.

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Question

(Modeling) Grade Resistance Solve each problem. See Example 3.

Find the grade resistance, to the nearest ten pounds, for a 2400-lb car traveling on a -2.4° downhill grade.

Accepted Answer

Welcome back. Everyone in this problem. A motorcycle weighing £450 travels negative 3.8 degrees down hill. We want to determine the great resistance of the motorcycle to the nearest point for our answer choices. A is negative £26. B is negative £27 C is negative £ and the D is £276. Now, let's make sense of what we're trying to figure out here. We're talking about a motorcycle riding down hill. So you know, I can't miss the chi the chance to draw a diagram, right? Of course not. So we have our motorcycle that's going downhill. Say this is the guy on our motorcycle. Let me just draw the motorcycle probably drawing. It wasn't such a great idea. Well, we have our motorcycle here and for our motorcycle is traveling at negative 3.8 degrees downhill. And that makes sense because it's going downhill and we know that our motorcycle is £450. If we're trying to figure out the great resistance, then the great resistance formula would be a big help. Recall that the grade resistance formula says that F equals W sine theta where F is our grade resistance, W is the weight of our vehicle. In this case, the motorcycle and theta is the great angle. Notice that we already have our, let's underline it here. We have our weight of our vehicle and we have the grid angle. So since let's write it here, since the weight of our vehicle is £450 and our great uncle equals negative 3.8 degrees. Ok, then we can substitute these values to figure out our grade resistance. So let's do that. This tells us then that our grade resistance would be equal to W which is 450 points multiplied by the sign of our grade angle, which is negative 3.8 degrees. To figure this out, we can put it into our calculator. Make sure that your calculator is in degree mode. When you put 450 multiplied by the sign of negative 3.8 in your calculator, you should get negative 29.82325518. And it continues on. But remember, we don't want all of these digits, we only want our great resistance to the nearest point. So that means we're going to look at the digit beside the pound, which is it. And since it's greater than five, we're going to round it up to negative 30 points. Therefore, our grade resistance is negative 30 points to the nearest point when we look at our answer choices that would have been answer choice. C thanks a lot for watching everyone. I hope this video helped.

(Modeling) Grade Resistance Solve each problem. See Example 3. Find the grade resistance, to the nearest ten pounds, for a 2400-lb car traveling on a -2.4° downhill grade.

Key Concepts

Grade Resistance

Trigonometric Functions

Force Calculation

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