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Problem 75 Hard Difficulty

A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 $\mathrm{m} / \mathrm{s}$ . Air resistance may be ignored. (a) At what time after being ejected is the boulder moving at 20.0 $\mathrm{m} / \mathrm{s}$ upward? (b) At what time is it moving at 20.0 $\mathrm{m} / \mathrm{s}$ downward? (c) When is the displacement of the boulder from its initial position zero? (d) When is the velocity of the boulder zero? (e) What are the magnitude and direction of the acceleration while the boulder is (i) moving upward? (ii) Moving downward? (iii) At the highest point? (f) Sketch $a_{y}-t, v_{v}-t,$ and $y-t$ graphs for the motion.

Answer

a) 2.04 $\mathrm{s}$
b) 6.12 $\mathrm{s}$
c) 8.15 $\mathrm{s}$
d) 4.08 $\mathrm{s}$
e)
i) 9.80 $\mathrm{m} / \mathrm{s}^{2}$ and is directed downwards.
ii) 9.80 $\mathrm{m} / \mathrm{s}^{2}$ and is directed downwards.
iii) 9.80 $\mathrm{m} / \mathrm{s}^{2}$ and is directed downwards.
f) see Graph

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Physics 101 Mechanics

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Video Transcript

since I have assistance is ignored the boulders and freefall and has a constant honor acceleration, equal toe acceleration due to gravity. But it's dawn lots. So let's stake this to be positive. Why access and this to be negative. Positive X axis on DH since yeah, Why is down In order to be negative 9.8 make up a second scrap. Now we applied a constant acceleration in questions to the motion off the border. So for thought, Gays, we have not right to be so. Then solve for party to find the time on they have they not white of the equal door, 40 meters per second. Um, wardens we have OK, that's it. And specifically for the first part, they have final velocity toa 20 meters per second. So the real news, the same question that involves all the variables are all the parameters that we are already given. So we will use this equation to solve for time. So this song good on DH, we get the value to be 2.4 Senor circuits. Make sure you use this negative sign while, uh, plugging this valium to this a question. 45 feet. You have three wide Toby. Negative 20. Meet up a second. So we will use this Sammy question to find the time. But with B y Toby negative 20 meters per second instead of positive 20 2020 meters a second. And this gifts t to be equal to 6.12 seconds. The Black Sea we have. Why mine it? Why not buy minus y not the week with Placido? They have as given initially. Leave me. I have we not y two b 40 meters per second. I'm gravity to be negative. 9.8. Meet a second scan not to find the time with balloons. Statistic question because we don't have to final velocity here. So we can't use this equation now because then we will have two unknowns time and rely to solve and we will be out ofthe questions for that. So we will use this equation since we already know all the perimeters needed to solve this equation for time. So that's Cape State of equal to negative. Totally not right over devises. Thiss fight goes to seed Oh, so it doesn't involve in the secretion on solving this We get timeto be a 0.16 seconds for Martine. We have they like you. We not. Why, Toby? 40 meters per second. Acceleration is negative. 9.8 meters per second squared on DH here we solve for time. So basically now, given the perimeters, we can again use this a question to find the time. So we do that we solve it using these values, and we can time tow vehicle tow 4.8 seconds on DH. Acceleration is obviously constant and is a call to 9.8 meters per second. But it points downwards. That's why we include the negative Simon solving questions. Now forge the last part. We have to draw the glass. Now. Uh, my gloves won't be exactly the scale because I don't have the necessary tools to join them. But this will give you an idea off how they should look like So time is and second, like solution, Miss Meat of the second Scotch velocities and meet up a second units distances and dollars. Okay, Now, as you can see from this equation by minus liner zero dismiss that the initial value off. Why is it called the fine and value on DH? If the start from the ground. I'll take mine. Ought to be zero. We have ID. Toby sees you as that. So now, as you can see from this equation without taking the y minus, why not tow Macedo? Let me just here is this now. So if you look carefully that this equation over here, you'll notice that this is a quadratic cushion off the time. So basically, this is off the phone. A x squared plus b x less he questions Edo all You can also say that this is a parabolic question. I know that. Why, Toby, My minus y not annexed to the tape. So taking that into account. So this graph should be a parabola. That why minus why not to be the same. And let's take them to a zero. This is why not? And and this is why. And the motion should be credible. Like so like this Now for the velocity horses. Time graph. We used this equation over here, so Oops. So as you can say, this is a linear question and this is similar. I do. Why? Equal to m express, See? But why is revived? Uh, M is the slow on DH corresponds to a guy here. X is your time and C is the y intercept in the graph which corresponds to the not quite so taking this this into account women flock. Bye now, Now, since V Why they not? Why is let me destroyed the question again. Now we have the slope, which is a light, Toby. Negative on. Be not. Why is giving Toby positive? This means that it starts from a positive value on DH. It can either go like this with a positive slope on like this. With the negatives. Nobody here slope is negative, so it should have a negative slope. This is the not white and slow with this. My acceleration is constant here, and their force acceleration is constant, but the first should be a straight line. But since its downward AJ this negative, it should be straight them the negative access. And this corresponds to negative 9.8. Now, remember that this over here can go all the way down because velocity can be negative because, uh, again have negative direction and therefore can be negative

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