For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics.

A car traveling at 30 m/s runs out of gas while traveling up a 10° slope. How far up the hill will the car coast before starting to roll back down?

Question

For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics.

A car traveling at 30 m/s runs out of gas while traveling up a 10° slope. How far up the hill will the car coast before starting to roll back down?

Accepted Answer

Hey, everyone. Let's go through this practice problem. A bowling ball is delivered before being rolled up an inclined plane, having an angle of 15 degrees with the horizontal draw a complete pictorial representation of the situation along with a motion diagram that will be helpful in finding the distance the ball covers before it starts to roll back down. Ok. So this problem is asking us to do two different things. Draw two different types of diagrams. First, we're asked to draw a pictorial representation of the situation. So let's start there. First, there's going to be first, I'm gonna draw the inclined plane. So that's the plane. I'll say this is the horizontal and there's an angle of degrees. And we're told by the problem that the ball is going to be rolled up the plane. So I'll draw the ball's first position as being right here. This ball is its initial position when it hits the slope and then it travels up for a bit before it reaches its final position before it has to, before it stops moving and starts rolling back down the inclined plane. So to represent this in variables, the ball's initial position will say X knot, its initial velocity is V knot and its initial time is T knot. The, the ball at the top, the final position will say X one, its final speed is V one and its final time is T one. The last thing I want to represent on the pictorial diagram is the direction of the acceleration. Now, you might think that because the ball is rolling up the slope, you might think that the acceleration is directed upwards. But here's the thing, the acceleration is actually going to be in the opposite of the motion here because of the fact that the ball is slowing down as it travels up the slope. Even if we're looking at the ball as it's rolling upwards, the acceleration is still going to be directed down the slope because it's the force of gravity that's pushing the ball back down the slope and and causing it to slow down before it finally starts rolling down as well. So the vector a the acceleration vector is directed down the slope. And this is pretty much all we can do for a pictorial representation of the problem. So now let's uh answer the second part of the problem and draw a motion diagram that will be helpful in finding the distance the ball covers. Now, basically the dis the difference between the motion diagram versus the pictorial representation is that for the motion diagram, we're gonna be one representing the dots the dots that will represent snapshots of the ball's motion at after each iteration of some time interval. So if I use this dot to represent the bowling balls initial position, then let's choose a time interval. Let's say we're looking at the ball's motion every one second. So there's one second between this dot and whatever consecutive dots are by it or adjacent to it. So in one second, the ball will roll up the slope by some distance represented by this arrow where we see the next snapshot. Now, as we established earlier, the ball is slowing down as it travels up the slope, as it travels up the inclined plane, it's accelerating downwards. So that means that in the, in the same time interval, the next dot It's going to be closer to this one because since the ball's motion is slowing down, it's unable to travel as far before that time interval passes, we'll draw another upward arrow except it won't be quite as long as the first one before we see the next dot And this pattern will continue, the arrows will get shorter and shorter as we travel up the slope. Before finally, at some point, the ball stops moving and starts help heading back downwards. So this is a visual representation of how the ball is accelerating down the slope. And this is really all we need to do to represent the two diagrams asked by the question. So we've basically solved the question and that'll be it for this video. I hope this video helped you out. I recommend checking out some of our other videos if you'd like to have more experience with these types of problems. And yeah, that's all for now. I hope you all have a lovely day. Bye bye.

For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics. A car traveling at 30 m/s runs out of gas while traveling up a 10° slope. How far up the hill will the car coast before starting to roll back down?

Verified video answer for a similar problem:

Key Concepts

Kinematics

Energy Conservation

Inclined Plane Dynamics