jack-mass-550-kg-is-sliding-due-east-with-speed-800-ms-on-the-surface-of-a-frozen-pond-he-collides-w

Name: jack mass 550 kg is sliding due east with speed 800 ms on the surface of a frozen pond he collides w
Uploaded: 2019-06-24
Duration: 7 min 1 s
Channel: Numerade
Description: Jack (mass 55.0 kg) is sliding due east with speed 8.00 m/s on the surface of a frozen pond. He collides with Jill (mass 48.0 kg), who is initially at rest. After the collision, Jack is traveling at 5.00 m/s in a direction 34.0$^\circ$ north of east. What is Jill's velocity (magnitude and direction) after the collision? Ignore friction.

Question

Jack (mass 55.0 kg) is sliding due east with speed 8.00 m/s on the surface of a frozen pond. He collides with Jill (mass 48.0 kg), who is initially at rest. After the collision, Jack is traveling at 5.00 m/s in a direction 34.0$^\circ$ north of east. What is Jill's velocity (magnitude and direction) after the collision? Ignore friction.

Ben Nicholson · Accepted Answer

problem. 8.39. We&#x27;ve got Jack and Jill, who apparently haven&#x27;t learned anything about safety from their infamous Hill adventure on a frozen pond where we can neglect friction, Jack is sliding to the east towards Jill, whose stationery and for this since Jack and Jill both begin with Jay&#x27;s, we&#x27;re going to call them and be anyway, it collides with her, and then we&#x27;re told that he goes off at five meters per 2nd 34 degrees north of the east, and we want to figure out what poor Jill&#x27;s velocity is its magnitude and direction. So because we can neglect the friction of the ice, this is a conservation of momentum problem. But to begin with, only Jack is moving. So it&#x27;s his Mass trans his initial speed, and we&#x27;ll call this direction X in this direction. And then, after they run into each other, we know that Jack is moving at his final speed for the X component. It&#x27;s going to be the co sign of data. They should not forget his mass because this momentum and then Jill&#x27;s momentum X component goes there. So Jack&#x27;s final element of his white component uh huh, like I should have a sign. And then the white component. Jill&#x27;s momentum, the live action. And so, for the sake of not trying to solve an entire vector equation all at once, we can break it into two equations. And solving those for the X and Y components of Jill&#x27;s speed are the components of her velocity. Rather, we find this is going to be the ratio of his best of her mass times, the change in his speed but in the development chain, the change in the relevant component of his feet. So be it. No, sorry. It&#x27;s, uh, a negative of change because you subtract the final from the initial is opposed to vice versa. Yeah, Now this works out to be four point for who? For seconds. Why component of Jill&#x27;s Velocity? Same story here. So because there&#x27;s nothing in the white component of Jack&#x27;s initial velocity, we just go straight to it being negative, and this is going to be negative. You, too, meters per second. So the magnitude of Jill&#x27;s awesome good to be the same old formula for the magnitude of actor. That has always been the case. This case is only has two components. All right, You think of it is having 1/3 which is zero because they remain on the surface of the frozen pond at all times. And so her speed is 5.4 six meters per second. And then so the tangent of her angle is going to be the white component divided by the component. And the angle then will be arc tangent of that ratio. Her angle wonder being 35.9 degrees south of these drawn here sort of intuitively. And then we saw lt&#x27;s like component. So that lets us know that this should be south of the East, and hopefully, this time they will learn something about safety and not keep getting themselves into these situations.

Paul A. · Answer

once again welcome to a new problem. This time we have to friends. So we have two friends on DA Um, they&#x27;re on a frozen pond. So, you know, one of one of the friends is moving eastward. So if you think about east west, not south. So this is not south. This is east, and this is West s. So one of the friends is moving eastward. And that&#x27;s, um uh, eighty kilograms. His name is some. So the mass off some. So this is some and some is moving eastward. The Marcel&#x27;s some happens to be eighty kilograms. So this is the information that you&#x27;ve given. Uh, you&#x27;re given that the moss off some is eighty kilograms and some is moving eastward this way. And then also, we have a big girl. Abigail is moving. Um, Abigail is moving northward this way. And well, given that the mass off Abby girl happens to be fifty kilograms, that&#x27;s the information that we&#x27;ve given The gonna collide off the ah, you know, after they&#x27;re gonna meet and collide. So both some and Abigail will meet and collide. So when they collide, some moves north east at an angle off thirty seven degrees you can sew. This angle will be thirty seven degrees and and then the other thing we have is Abigail moves south east this way, and she&#x27;s going to move at an angle off twenty three degrees. That&#x27;s what happens. We can extend that for purposes off, finding solutions to this problem and the other extra information that given other than the fact that these two angles So this is thirty seven degrees and this is also twenty three degrees were also given that the some is going to be moving with a final velocity. You know, the final off six made us the second, and an Abigail is going to be moving southeast at twenty three degrees with the final velocity. So this is this is final velocity of some. So, you know, we should change the labeling right there. So we&#x27;LL say, uh, you know, sums final velocity And this is a big girls final velocity. So I&#x27;ll be girls finally lost his nine point zero zero meters per second and so we want to find input. A. So all that&#x27;s the information that&#x27;s given, So we want to find in part a of this speed before collision a speed before collision. That simply means that there was an initial velocity for some. And then there was also an initial velocity for, um, happy girl. So those are the two numbers. We want to find out the initial velocity of some on the initial velocity of the other girls. And then the other thing we want to find out this is in part B. And what do you want to find out the, uh, the decrease in Connecticut. Okay. We want to find out the decrease of the the decrease in kinetic energy in the total Connecticut Andy Uh uh. Off both of them. That&#x27;s the information will given the fast thing we&#x27;LL do is think about the movements after collision in the X and the wind direction. So, in the ex direction we have of the the last e final velocity off some co sign thirty seven degrees. And then we also have final velocity off Abby girl co sign twenty three degrees. That&#x27;s the in the ex direction in the white direction. Some is going upwards. Okay, so some is going up. What? We should have had this, you know, a little bit lost so you can get to see some of these variable resolutions. So that&#x27;s, uh, some Some of this would be a final velocity off some sign off any servant that&#x27;s in the white direction and then for Abigail, it&#x27;s negative because of the South, his negative north, his positive East is positive. West is negative. So this is negative. Final velocity of Barbie girl Sign off twenty three. So that&#x27;s what we have so gonna find Apply the law of conservation of momentum law off Conservation of momentum both in the X in the white direction both in the X and the wind direction. So we&#x27;LL say, um you know, full, uh, in the ex direction I will say the initial momentum in the X equals to the final momentum in the X the initial momentum in the ex who only have some So, um, ourselves some times the initial velocity of some ask the equal the the X direction the final ah, muss off some time&#x27;s final velocity off some in the X and then plus moss off Abigail Time&#x27;s final velocity ofthe other girl in the X Direction. So goes to find the initial lost your son and that just comes by dividing all these numbers. So you know final, we&#x27;re going to do that in the next spade. So for purposes off, continuation of we get final velocity off some no initial velocity of summers. You, Khun C. I&#x27;s going Toby Mass off sometimes final velocity of some in the ex direction causing thirty seven plus muscle. Abigail Time&#x27;s final velocity of a bagel in the ah, in the ex direction. And then we&#x27;re going to divide all of that by thiss value here the mars off some. So that&#x27;s the information we were given eso When? When we plug in these numbers, massive sum is eighty kilograms. Times of the final velocity of some is six meters per second. Ah times co sign off thirty seven and then plus uh, masal a beagle fifty kilograms. Time&#x27;s final velocity off baby girl is ah nine. Remember, we&#x27;re given Faz nine meters per second, so this is nine meters per second bond. Then times co sign off twenty three degrees on. We have to divide all of that by the mass of some, which is eighty kilograms. So we play in the numbers just to make sure we&#x27;re doing the right thing. So eighty times, six times co sign off the D Servant plus fifty times nine times we&#x27;LL sign of twenty three. Come on, then all of that divide by eighty and it gives this nine point nine seven. So that&#x27;s the initial velocity of some happens to be nine point nine seven meters per second. Ah, that&#x27;s what we find that on then the next big want to do for Abigail And now, using the conservation off momentum in the white direction, we&#x27;re saying that the initial momentum in the Y equals to the final momentum in the UAE. Initial momentum in the y. Remember this time we have Abigail the wind direction going up. What? Some ass off, Abigail Times initial velocity of a big girl because to mass off some times, final velocity off some in the white direction. So sign off thirty seven. And then we also have a component for every girl. So mass of Abigail Time&#x27;s final velocity of Abigail. This would be sign of twenty three, so t yet the initial velocity of a big girl, we have to take ah the final momentum in the white direction for some and then minus the final momentum in the white direction for Abigail, remember, the girl is going in the opposite direction, so ha momentum is minus negative. And then divide by the mass of Abigail. Gonna plug in the numbers. Massive sun is eighty kilograms, eighty kilograms times velocity of some six point zero zero meters per second. Sign off thirty seven a minus mass off my big girl is fifty kilograms. Um, the final of the last year&#x27;s baby girl is six. Made us the second sign off twenty three all of ah, Marcel&#x27;s a big girl happens to be, Ah, fifty kilograms. So when we plug in the numbers, we get that thie initial velocity of a big girl happens to be two point two six meters. Yes, I can. So that&#x27;s that&#x27;s what we have right there on. Then in the next page will look att, the kinetic energy. Um so you know, we&#x27;LL see the change in the change in Connecticut energy for some So we&#x27;Ll do the change in Connecticut energy for some And this one becomes, uh, dull telekinetic energy. Some is, um final kinetic energy for some so sums final Connecticut and you mind the sums initial kinetic energy. So this is one half em of the final, Uh, can I, the Kennedy for some minus squared minus of the initial kinetic energy for some initial. So we need to change this a little bit. No. So sums initial squared, and so we plug in. We have This is massive sums off eighty eighty kilograms. Time&#x27;s final velocity of some is six meters per second squared minus. Initial velocity of some is nine point nine seven meters per second squared. And that gives us a negative energy changing kinetic energy. And then we&#x27;re going to do the same thing for Abigail. So, you know, change change in kinetic energy for Abigail because to the final kinetic energy for Abigail, minus the initial kinetic energy for other girl, which he calls to one half em. Abigail V. Abigail Final squared minus the Abigail initial squared. And so we plug in the numbers masses fifteen point zero kilograms and then times the velocity is the final velocity for Abigail is nine meters per second squared on DH. Then we want a minus, you know? So just make sure this is this is different right here. so they don&#x27;t collide. And then minus the initial velocity of Big Girl, which is two point two six made us the second we competed that in the previous apart on. Then when you simplify that, you get negative. Six hundred and thirty nine jewels. So we have to combine the of the change. The total changing kinetic energy becomes change. Sure. Some minus change for Abigail, which is negative. Twenty three twenty five, three, six Jules plus. Ah! Oh, you know what this this was This was supposed to be our big girls. This is a big girl. So you want to make sure that we have the right numbers right there? So this is one thousand eight hundred and ninety seven point three two jewels. And so that&#x27;s the number we&#x27;re going to put in right here. Eight one eight nine seven point three two jewels. Um, yeah, and that ends up giving us negative six thirty nine jewels. So we combine these two Ah, the change in Connecticut. For both of them, um, the total change in Connecticut so immense that the decrease the decrees in Connecticut aji is six hundred and thirty nine jewels like that hope you enjoy the problem. Ah, feel free to send any questions my way and have a wonderful day. Okay, bye.

Sri Datta Vikas Buchemmavari · Answer

So in this problem, Sam, off late 80 kilograms, it&#x27;s moving with some velocity East toys on Abigail is moving with. We&#x27;ll ask the 50 killers. I&#x27;m sorry with Mass. 50 kilograms is morning with some velocity, not work, and they collide. And after the collision, Sam is moving at an angle of 37 degrees. Not a beast on Abigail is moving at an angle 23 degrees south of history with velocities six meters per second for Sam and nine meters per second for a beginner. Remember that the masses are 50 kilograms and 80 kilograms for Abigail and Sam on. We want to find out their initial velocities. Let&#x27;s say sounds, initial velocity is we&#x27;ve gone on. Abigail&#x27;s initial velocity is 32 now. We simply use consideration off Wyndham in this problem. So initially they went to the next direction is simply the moment off, Sam, because Abigail&#x27;s motion is in the vertical direction. Remember that I usually are X axis in the horizontal direction on why access is in the vertical affection and work this coincides with not on except this construct coincides with the east now, initially, the X the moment when the extraction is simply the momentum off Sam, which is mass. 80 kilograms times velocity people. But after the collision, the moment of the next direction is this Sounds off the ex moment death excellent. Off Sam and I begin for Sam the moment and will be mass. 80 kilograms times velocity six meters per second times cost 37. We got data would be the re x, the X competent off the velocity off for Sam and for Abigail the ex confident off the lost momentum would be mass. 50 kilograms times speed, nine meter per second times cost 23 degrees. Now because there are no other forces on the system, you know that they need a moment. The initial momentum is equal to the final moment about the total system, which gives us a TV one is equal to 80 times six times cost 37 less, 50 times nine times past 23 degrees. Solving this we get everyone is equal to 9.97 Meet a person. Similarly, we used a conservation of wondering why direction To see the initial moment of in my direction is simply the momentum off Abigail, because Sam&#x27;s emotion is in the extraction, and that could be a mask. 50 kilograms times you lost if we do and which means the final Y moment in the white direction would be divine. Move off Sam, which would be in the upward direction and that would be mass. 80 kilograms dangled times velocity six. Fine Scientist just signed 37 degrees. This would be the three white, the white component off the last 2% for a now. For Abigail, the velocity would be the moment of wide Alex. In the white direction would be masked, which is 50 kilograms and philosophy, which would be nine meter per second and then signed 23 degrees. But not that defy component is in the downward direction because our Tita is actually clockwise direction. And instead ofthe blessed sign, we have a minus sign here are using this to equation against because initially went missing the final moment because there are no external forces we have veto times 50 is equal to 80 times 60 signed with his own minus 50 times nine dying signed 23 which gives us we do is equal who point to six meters per second. Now that we&#x27;ve found the velocities. We want to find out the amount ofthe indignities last year in the collision. No, that would simply be the initial kinda country minus the final kind of energy. Now the initial kind of city is this something autocratic? Energy&#x27;s off Sam and Abigail That would be half times mass, 80 kilograms and velocity squared. We want square, which would be 9.97 squared less candy candy off Abigail, which would be half thanks mass 50 kilograms times we do square, which is 2.26 square minus the final Kinetic energy is simply the sums off the final kind of energy&#x27;s off Sam and Abigail here, and that will be half times mass. 80 kilograms. I&#x27;m six squared, let&#x27;s have. And for Abigail times 50 times nine squared. The initial kinetic energy turns out to be the sum of these totems. 400 4,000 104. Jules, on the final kind of guarantee, some of these two times turns out to be 3,465 jewels, giving us the total change in kind of energy. 639 jewels. Of course, if you define your change in Canton County as the final minus initial kind of energy, there will be a minor sign here. Regardless, we know that this amount of energy has been lost from the form off. Frantic energy on this much energy will be converted into some other kind of energy like he

Julie Farhm · Answer

we have to ice skaters in this problem. One that is 50 kilograms. Make a stick figure. 50 kilogram ice skater. I&#x27;ll put ice skates and that skater is moving to the east with the velocity of three meters per second. And then we have another ice skater that 70 kilograms moving at a velocity of seven meters per second. So 70 kilograms think they go to 36 eggs. So clean this one up here, 50 kilograms and 70 kilograms. And this one is moving with a speed of seven liters per second. So they meet, they joined together and they move off at an angle and in a different velocity. So we need to find both the speed in the direction that they move off together. So we need to find the momentum of each and will draw separate momentum diagram. The momentum of skater won initial momentum of skater One is going to be 50 kilograms times three meters per second and that is 150 kilogram leader for second, keeping it to three sick pics. Then we have my initial momentum of skater to which was 70 kilograms times seven. I&#x27;m dropping my zeros because I&#x27;m out of space here seven meters per second and that gives us a initial momentum off 490 kilogram meter for a second. But this one is east and this one is south. So we draw this diagram like this. P initial one is 150 and p initial too, not to scale realized. That should be longer P initial to 490 kilogram meters per second. So we need to find the total momentum because the system has no external forces. The total momentum before and after the Cleveland will be the same. So if we have something moving to the right and something with the east and something moving south, this is our total momentum vector here, from the empty tail to the empty head. So using first, let&#x27;s find two parts of this. You have a total them into magnitude, and we also have a direction because the direction is the first thing that the problem asks for it. Let&#x27;s find that one first. Um, it&#x27;s a right triangle. This is a 90 degree angle. This is the opposite for 90 and 1 50 is the adjacent, So the tangent of the angle. It&#x27;s going to be 490 divided by 160. So to solve that angle, we used inverse tan of 4 90/1 50 and plug it into your calculator. That&#x27;s negative. Sign there you get 72.98 degrees around it to 36 bigs. We have 73 0.0 degrees, and that would be south of East, because the direction that scare one was going was east and were quickly going south of that. So that&#x27;s the first part of the problem. That is the angle for the second part of his velocity. So we need to find the total momentum vector. Here. We can use the factory damn to find the magnitude of P total we can do 150 square plus 490 squared is the magnitude of P total squares. So P total comes out to when you add them the squares together and take the square root 512.4 kilogram beater for a second. Then we know that that&#x27;s gonna be equal to the total mass times the final velocity because that is the mo mentum. We have now two things stuck together. So the total mass is gonna be the massive Skeeter one and the massive skate or two. And the massive skater one is 50. The massive skater won a seven days so that total mass is 120 tens of the final is equal to 512 weeks for so 512.4, divided by 120 gives US 236 Biggs 4.27 meters per second. So the skaters move off with a speed of 4.27 meters per second in a direction that is 73 degrees south of east.

Sarah Mccrumb · Answer

side Ready Scitex and Liberty to write out some things for us. For this problem, we have a mass of a skater of the problem. A 65 kilograms. The velocity is 2.5 whose per second, 0.150 kilograms for the snowball and a velocity of 32 meters per second. So for this we&#x27;re gonna do the first part and we end up with We&#x27;re gonna take the 2.5 meters per second out and we&#x27;re gonna add 65 kilograms plus 0.15 kilogram. And we&#x27;re also gonna have equal to 65 kilograms times the velocity. We&#x27;re trying to find claws. There you go, Eric. I want choice, please. Everything in? Yes, on What we&#x27;re gonna be doing is just solving it. The math here for you guys. So let me just put everything in my calculator here. I mean, up with one 65 0.875 kilograms Meters, four seconds. I&#x27;m sorry. My s is help, like five sometimes there we go. Minus it. Would a minus this right here for us because, um, he keeps things a little bit more. Ah, simple. When we do that so minus 4.8 kilograms. I&#x27;m not sure what I did to get that giant liner here, but it&#x27;s open, and we&#x27;re gonna McKnight ass a little bit better for you guys. There we go. Unless equals 65 kilogram philosophy. And I&#x27;m just gonna do this really quick. Actually, this is 62. I don&#x27;t know why I wrote that wrong. Even though I have my calculator at year. But it&#x27;s okay. We caught it. And what was gonna dio is 1 58 0.0 75 divided by 65 kilograms. And these kilograms, we&#x27;re all gonna council out. Yeah, and we know with Silver Second, and that&#x27;s gonna be our velocity here. And that&#x27;s gonna equal point for three meters per second. And that&#x27;s hard to answer now. Uh, a second suitor on the second skater is mass is a kilogram, and the missile is a hero. And because of that, we are having 60 right here. I would have the snowball first on the left hand side of the place and that we did above So having 0.1 by Phil Gramm of a snowball Heinz 32 years per second. Now that&#x27;s gonna be equaling you. And we have a B F A final and yet six waas massive the I wanna put kilograms. Yes, You guys know that I&#x27;m not forgetting that now you can just simply multiply things together. So get 4.8. You&#x27;re kilograms, meters seconds because the and this is gonna be 60 0.15 gram and kilograms canceled. And our answer is good be when we divide 0.1 7 98 with is your 0.8 second and this is our second answer.

Joseph Petrullo · Answer

So for this question, all we need is the X equation. So initially we have some mass be with some velocity be. And after the collision, it sticks to another block and it moves off with some velocity V f and in some direction. And so the X component will be the co sign. And since it moves north of west, this data will be 1 80 minus 42.5, which is equal to 1 37.5 And so now we have everything that we need in this. In this problem, all we have to do is solve for VB, which is equal to M a plus MB times, VF times, the co sign of 1 37 0.5 divided by MBI and plug in the numbers on this problem. You should get that VB is equal to minus four meters per second, where the X direction is defined as follows. And that&#x27;s the answer to this question.

Problem

To protect their young in the nest, peregrine fal…

Problem 39 Hard Difficulty

Answer

$v=(55.0 \mathrm{kg})(5.00 \mathrm{m} / \mathrm{s})\left(\sin 34.0^{\circ}\right) /\left[(48.0 \mathrm{kg})\left(\sin 36.0^{\circ}\right)=5.46 \mathrm{m} / \mathrm{s}\right.$

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$v=(55.0 \mathrm{kg})(5.00 \mathrm{m} / \mathrm{s})\left(\sin 34.0^{\circ}\right) /\left[(48.0 \mathrm{kg})\left(\sin 36.0^{\circ}\right)=5.46 \mathrm{m} / \mathrm{s}\right.$

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Liev B.

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Math Review - Intro

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Hugh D. YoungUniversity Physics

Liev B.

Farnaz M.

Aspen F.

Meghan M.

Hugh D. Young

University Physics