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A 747 jetliner lands and begins to slow to a stop as it movesalong the runway.If its mass is 3.44×105 kgkg, itsspeed is 75.0 m/sm/s, and the net braking forceis...

Question

A 747 jetliner lands and begins to slow to a stop as it movesalong the runway.If its mass is 3.44×105 kgkg, itsspeed is 75.0 m/sm/s, and the net braking forceis 4.30×105N4.30×105N, what is itsspeed 9.00 ss later? Express your answer using three significant figures.How far has it traveled in this time?Express your answer using three significant figures.

A 747 jetliner lands and begins to slow to a stop as it moves along the runway. If its mass is 3.44×105 kgkg, its speed is 75.0 m/sm/s, and the net braking force is 4.30×105N4.30×105N, what is its speed 9.00 ss later? Express your answer using three significant figures. How far has it traveled in this time? Express your answer using three significant figures.



Answers

Stopping a 747 $\mathrm{A} 747$ jetliner lands and begins to slow to a stop as it moves along the runway. If its mass is $3.50 \times 10^{3} \mathrm{kg}$ , its speed is
$75.0 \mathrm{m} / \mathrm{s},$ and the net braking force is $7.25 \times 10^{5} \mathrm{N},$ (a) what is its
speed 10.0 s later? (b) How far has it traveled in this time?

They are with speed in the case of uniformly accelerated motion as equals God. Initial speed to be a That's the final speed we have upon to. Okay. Ah The initials food via is a covering Too two and two. The average velocity minus the final speed beef. Since the fund speed is zero, the initial speed we are is it comes to two and two. The average velocity that is 37 kilometers. What are the initial velocities? 70 kilometers. Mhm. Other acceleration? Well, we can write the initial velocity is -70 into five upon 18 m four seconds. Are the initial well, as it is 19.4 meters for a second. Now, the average acceleration is equal to the final velocity. Minister initial velocity upon the time. T Are the average acceleration is the vulnerable city, zero m 4 seconds minus minus of uh -19.4. We just for a second Upon the time to seven seconds Are the average acceleration in this case is 2.77 me, just four seconds.

Here. Religious. Be usable toe 800 meters per second. Jet lands bill physical to 900 kilometer. But our number off engines are three. And here he is proportional to be zero Squire. Or you can say that damage A is proportional to the initial velocity off the square So I can write these equal to okay into these. Quit. Okay. Now, in order to calculate the speed off the airliner after it has lost the use off engines, we have to write the balance equation off the airliner in cars direction with cursing spade. Busy group within three engines are within number three. So for this again, rage, if minus is a cordial Tzeitel. Let's see. Digression number one, this one we're going to use for for the calculation. Okay, Now, let's simplify the time so I can write f is acquittal endgames the M Open DT u minus vo. Okay, now we will put all the values here there and is equal to three. The embodied et as we know you is 800 we always 900. But here view is in Dems off, um, our kilometre forever. So we need to calculate it in terms off me. Double staking So all I can write his three b m or born DJ you is my 800 minus 900. And to convert it into meter per second, I will manipulate the strong by toes ing and divided by 3600. Okay, so my final value will be 1650. Jiang's the, um upon need you thirties if Okay. Noto calculator to D As we mentioned in the elbow, immigration D is nothing but gear times residual square. So, do you use equal to get James thinking in studio? Let me jump. But are we need the unit major per second. So everybody playing the stone Tozer in the word bay 3600 to 900 square. And my answer will be 62 chosing 300. Okay, this is nothing but devalue Looking, moving. Put another substitute This f end the into equation number one, which is nothing but f minus days Acquittal zero. So from that, I'm able to get DDM upon DT so I can write my the m A born d d is acquittal 30 serving point. It does in 780 age Dymski. Okay. Moving further and talking about the first part. Now dispute off the Lehner after it has lost the use off one off its engines with cars. Things for you to be by. And let's say it is losing the engine one. So now our total engine will be too. So I can rage and musical due to. So let's read The formula for F is a cordial end. James the M A porn DT James U minus Very to no, we will put all the values here. So I will have door 37 point. You did seven. You do you do you? You do. You turn Drood minus. Were you going? Sorry. Please make the correction here. The Germans were even nor the vigil. Okay, No, let's simply for further and use the equation. One, we will get Jourdain's 37 brains. It's seven h age key. You turn Drood minus really one miners. You've even squared as we know. This is the after, and this is the detail and the is equal to Gavey Square is Acquittal zero. This is nothing but my equation number one. Okay, No. After simplifying, Ivory Gate even is equal to 211.2 major per staking similar calculation we can do for the second part and we cane get the values off Me too. So it's moving towards the second mark in that case, it losing two engines. So here we are dealing with only one engine and my any will be one. This is their different. So I can write my formula for force a physical job and there it is. One times bmo Porn DT that is 37 point 80 7 80 age name Ski into you. There it is my 800 minus Rayvon Sorry. Minus Rito. Okay. And we are applying this ever into equation Born again. So according to Gration, one F minus three is equal to zero We have the F equation and as we know days equal to nothing but get into B two square. So Novia, using the student into the Grecian born and simplifying you'd we really gate the velocity V two is equal to 156 point 17 major per se King

We have an object with a nine kilogram mass. Okay, the resist of force is negative BV. So it's going to reach half of its terminal speed. So I'm going to write t half in 5.54 seconds. Um Well let's figure out what it's terminal speed is. Uh some of the forces equal mass times acceleration which is going to be M g minus BV. So A would be g minus BV over em now um when the acceleration is zero, that is the terminal uh speed. Rearranging that V would be Gm over B. Okay, so it's going to reach half of its terminal velocity. It's gonna be Gm over to be okay, determined that terminal speed. Okay, determine the terminal speed. Well, I don't know B So yes, so I'm either going to have to use some numerical modelling or I uh differential solve the differential equation. Um and actually I remember in the book that it did give an answer by solving the linear differential equations. So I think I am going to take that route um numerical modeling here. So it says that the answer it involved an ex opponent. I'm just trying to to find it. All right. It's gonna take me a little longer to find it. Yeah. All right. So it was given to us On page 165. And you figure this out using solving the partial differential equation. Um So let's see here. V equals M. G over B Times one -E. To the negative. Bt over empower. Okay. So um what was I trying to do this? Okay. What is the terminal speed? Well, in order to find the terminal speed I have to know what B is. Okay, there we go. So mm and I know t to be at one half. Okay, So Gm over to be Which would be the at half. Would be M. G. Over B times one minus E. To the negative. I be over M. T. One half. Okay G cancels out. M cancels out be cancels out. So now I get one half on the left and if I subtract one on both sides, that would be negative one half. So one half is going to equal E. To the negative be over em t to the one half power. I mean T one half not half power. Okay, So now the natural log of 1/2 is going to be negative B over em t one half. So B is going to be negative M. Natural log of one half negative M. Natural log of 1/2 over T half. Okay, so let's put that in a calculator. I don't think I put anything in a calculator yet for this problem. Okay. Em is nine Okay. Yeah. Um He half is 5.54. Okay, so B equals negative M natural log of one half. Which does give a positive number now, negative times negative positive. Um divided by T. That's going to be 1.1 26 And I'm gonna call this tea sub zero just so that I can use T At a different time. Okay, so B is 1.13 now. We did want to figure out the terminal speed with the terminal speed is Gm over. B. G equals nine eight one. So GM over B is going to be 78.4 meters per second. Okay. At what time is the object? 3/4 of the terminal speed. Okay, well this is half of terminal speed here. So for 3/4 of terminal speed, three force would equal one minus E. To the negative be over em t. Okay So 3/4 -1 Is negative. 1 4th so 1/4 equals E. To the negative be over. Mt power. Natural log of 1/4 is going to be negative be over. Mt So t is going to be negative M over B Natural log of 1/4 negative M over B. Natural Log of 1/4. So I'm trying to get to the calculator. There we go, negative. Mhm mm Over B Natural log Of 1/4. That would be 11.1 seconds. How far has the object traveled? In part A Okay, so we've got velocity as a function of time right here. So I'm going to write that down. V equals M G over B. One minus E. Do the negative be over em T. Power. I am over M G over B. One minus E. To the negative be over. Empower times. T Okay now I'm going to distribute the M. G over B. Okay, so I'm gonna do the integral of this now. So I'm going to let you equal negative B over em T. Then do you is going to be negative B over em D. T. So I want to do the integral of this. Um D. T. So now the integral the velocity is a position MG. T. Over B plus. Now I've got um D. T. I want to solve this for D. T. Is gonna be negative mm over B. D. U. Okay, plus then I've got negative M over B. Times M. G. Over B times E. To the U. Power D. You. Okay, so why is going to equal MGT over B minus mm square G. Over B squared E. To the U. Plus a constant. But you is negative B over Mt. So I can put that in there. All right. Now, initially what is this What's going on here? It falls from rest so V. of zero is 0. But why of zero is something? How far is the object traveled? Okay. So let's just say that Y. Of zero is zero. But If why of zero is set to be zero. Even the zero is 1. Then see would be M square G over B squared. So why is going to be MGT over B minus mm square G over B squared E. To the negative. Be over M. T. Power plus mm square G over B squared. Okay. Now, um just making sure I didn't lose my negative there. No, I didn't. Okay, So now we need to figure out At 5.54 seconds. So, mhm. MG. over B minus M squared G over B squared E. To the negative. Be over em t zero plus mm squared G over B squared. Okay. That seems like way too much. 700 40 seven meters. Mhm. I mean it's not unreasonable if this is a rare with a slightly viscous medium in it. Um So what was it before I put in that last term? Only 121 but then I put in that term um Okay so wait a minute but I said why of zero needs to be zero. Okay, but this is not zero. Um If I set this to zero Then this should be zero. It's undefined. So maybe I'll put it at 0.01. Yeah, that's zero. Okay, so that does seem right. It goes from zero two 5.54. Where is it? Here? It is. Yeah. 740 eight actually, meters. Okay. Everything made sense until we got down to this. It takes 11 seconds to get to 3/4 of the terminal velocity, and the terminal velocity is really high. So, this should be a very high number. If that's really the terminal velocity 74, m/s. So the terminal velocity is Gm over B. Since B is a tiny number, it's not terribly tiny. And I just want to verify terminal velocity is Gm over B. Which is correct. Okay. So, I think I mean can if this is right up here Where it says the 11 and whatever here, and if this is right, well then this does make sense down here. All right, thank you for watching. Good luck.

Hard. In the given problem, a nine kilogram object is falling down under it's Sweet MG and are resisting force, which is given by our is equal to B times softly. There really is the velocity off the object at an instant as the sign. Even here, it's negative. It represents that this business t force in a direction off opposite to the direction of motion. So now the values given here are mass off. The object is 9.0 Did you velocity? It achieves in a time 5.54 2nd is equal toe half off its terminal velocity and we have no find the final terminal velocity achieved by the object. So if we use the equation off motion, this is mg miners be re is equal toe any But in case off the final velocity, if we become sweetie, which is a constant velocity, so acceleration become zero so we can see m g minus B VT will be zero or you can see the expression or terminal velocity is m. Times of G, divided by beat B is a drag coefficient. No, you know, expression for instantaneous velocity achieved by the falling object in terms off terminal velocity is given us We is got govt multiplied by one minus e based on the par minus t divided by tell you about Mr Pine Constant which is given us the ratio off em muscled object with her black coefficient. So when they put all these values off meaty and how etcetera here we get, we is equal to n times off GT invited by B multiplied by one minus Edith's to the problem minus B in 30 divided by em. So it has been given that ri is going toe half off Pretty same place off we we can put m times off g divided by doobie And here in the right inside is equal toe mg by B one minus e but issued a par minus b be divided by masked off the spherical object This m G and B Really cancer leaving behind just, huh is equal to one minus e missed the barber minus b he buy em. So this edict bar minus b B by em becomes equal toe have so we convert it now in the logarithmic form. So we get BT by m is well naturally Gary, them off to. So here it becomes the ratio Mbai be is equal to okay. Divided by natural Garrod. Um, off too. And we know the time is given us 5.54 2nd and naturally carried them off to comes off the 0.693 So here it becomes 7.99 seconds. So now, using the expression for terminal velocity, it is given us m into G by B. And we know now the value off this Mbai be so using it, we get to know this is 7.99 2nd into 9.8 meter or secondly square. So finally it comes out to be 78 point three meter per second. So this is the answer for the first part of the problem that the terminal velocity of this object will be 78.3 neater or second answer for the first part of the problem, No. In the second part of the problem, we have to find time taken by the object in order to achieve the final velocity as 3/4 off its terminal velocity. So again, we will use the same aggression. These goto et one minus heated to the problem minus b Buy em into T. So here it becomes. Three by four is equal to one minus e Finished the barber minus B. Buy em in 30. So this e bishop ar minus b buy em into T comes out to be one minus three by four. Or we can say this is one by four. So when we convert it into logarithmic form, it becomes be times be derided by em is equal. It'll natural gas Leedom off four. Or we can say the time is equal toe m by be in tow Natural Garrett um off four all 7.99 into 1.386 seconds. So finally, the answer. For the second part, the time taken by the object in order to achieve 34 from terminal velocity is 11.7 Second, this is answer for the second part of the problem. Finally, for the third part of the problem, we have to find the distance taken by the object in time 5.54 seconds. So time here is five point by four. Second and using the standard expression, the distance are covered by the object will be given by integration off re DT. As you know, the distance is equal to skating to die and feel the dime. The speed is variable. It is in the form off and speed is given as a function of time. So this is the speed integration off. This is speed having a range from zero to be for the time. So they put these values, you know, expression for this instant innocents beedies GT one minus e minus t by down big having a range from zero duty. So this integration comes out to be witty as a constant Marlys d plus No, he'd issue bottom minus steed by doe minus one limits again from zero to t. So we know the value. This terminal velocity this is 78.3 and the values off the time from zero to high 0.5 For when we put these values we get for me this is 5.54 for power, for time Constant. This is 7.99 for e race to the bottom minus D by how time is again 5.54 For now, this is 7.99 minus one and finally this complex calculation comes out to be equal to 121 meter. Thank you


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