bullet-on-a-very-muddy-football-field-a-110-kg-linebacker-tack-les-an-85-kg-halfback-immediately-bef

Question

$\bullet$ On a very muddy football field, a $110-$ kg linebacker tack-
les an 85 -kg halfback. Immediately before the collision, the
linebacker is slipping with a velocity of 8.8 $\mathrm{m} / \mathrm{s}$ north and the halfback is sliding with a velocity of 7.2 $\mathrm{m} / \mathrm{s}$ east. What is
the velocity (magnitude and direction) at which the two players move together immediately after the collision?

Sri Datta Vikas Buchemmavari · Accepted Answer

So in this case we have to footballers a linebacker with weight, 110 kilograms on velocity, 8.8 meters per second and 1/2 back going with the velocity 7.2 meters per second and max 85 kilograms. They both collide at a certain point on DH, then start moving together in some direction. Let&#x27;s say this direction makes an angle ofthe theatre with the horizontal and the velocity would be something we obviously the mass would be the sums off the two masses one ten 10 plus 1 85 and that would be 195 kilograms. Now, as usual, will choose exactly horizontally and y axis vertically. We want to find out the magnitude of the velocity and the direction, which means this angle. So now let&#x27;s say this velocity has to conference. I mean, obviously it has to confidence re X and B. Bye, Right? We y on the X now release conservation of energy in two directions X and Y delusions to find out the X and y now initially going for X direction. The initial what went on in X direction before the collision would be simply they went off the halfback because the line doc&#x27;s going down linebackers mourned him would be completely in the vertical direction. And they have that morning movie mask 85 kilograms times the last e 7.2 meters per second. Now the final momentum in the X axis in the extraction would be masked off the off. Put the players times the ex con print off the velocity on mass off what the players would be. 1 95 kilograms and the velocity would be pX. And because there are no other external forces and friction is negligible, we can say moment of his guns out and hands if the initial and finally moment does Melinda in the X axis the extraction all the same. Which gives us the X Times 1 95 is equal to 7.2 times 85 calling this equation forget we accept equal to 3.14 meters per second. Now for similarly for why access? The initial moment of in my direction is simply the momentum off the heavier player. That would be masked Time&#x27;s philosophy 8.8 meters per second. Now the final momentum invite direction would be the mass ofthe other players multiplied by the white component of Velocity v i. Viv I. That would be 195 times. We buy again using conservation of momentum we see 1 95 is equal to 110 multiplied by sorry, 110 multiplied by 8.8 This cues Levi is equal to 4.96 major over Sigan Now that we have got to leave what on the ex? We can see that the magnitude of the velocity V is simply wrote off. The X squared plus y squared is in the fight about in the room and this turns out to be 5.64 meter per second. Now, as far as the angle ghost we know the Tita you stand in worse off B y by the X, the white continent of velocity divided by the ex confident of velocity. It&#x27;s turns out to be 57.7 degrees, just 58 degrees. Use only two significant digits because our velocities I have only to say David indigents. So this combined the two players together, who at the velocity off 5.64 meters per second at an angle of 58 degrees not off east

Ben Nicholson · Answer

problem. 8.37. We&#x27;re told of a football tackle that&#x27;s occurring on a very muddy field. And so the players are able to slip around without much friction that we need to worry about, at least for the duration of time. Immediately, before and after the tackle. That&#x27;s in question. And so we&#x27;re told that a linebacker is moving, uh, north at this speed and that this mass towards the halfback was moving east with the given speed mass. And then we&#x27;ll have what we call T, I guess, for the tackled pair of them moving off some direction north and east with the combined mass of 195 kg. We want to know the magnitude and direction of this. So because the any forces acting external to these things are going to be negligible for the situation in question, he conservation of momentum applies. So before the tackle, we have the let&#x27;s do this one first because we&#x27;ll call this direction X this direction, why we can just call them East and West, you know, So the X component first is going to be the mass of H times. The initial speed of age and the exhale direction and then l is going to be moving in the Y direction. Oh, initial. Why direction? I didn&#x27;t. This is going to be equal to the final momentum where the Mass was going to factor out it here and we&#x27;ll have the X component of the final velocity. Unsurprisingly enough in the extraction bus, white component of the final velocity, the Y direction. So then we can we can solve this. This is technically because X hats and white hats don&#x27;t add together and the amazing uniform we could have written This is a system of two equations and in fact, we can make found the final student the extraction going to be the mass of halfback times. So both the half backs and it&#x27;ll speed and provide component. They&#x27;re like carbon farm, the linebacker with no created on his otherwise right. So this works out 3.14 m per second and this is 4.96 Yes. Now, to find the magnitude of this, of course, this is always going to be just the some of the squares of the components and then take the square root of that and that works out to be 59 m per second. And then if we call, we take the direction the angle north. It is from the east because that theater that will be the arc tangent of the ratio of the Y component of the velocity to the extent and to remember how to do this. Imagine we have any vector you like, which, in this case, we could be for velocity or for vector the X Yeah, data. And then we know that the tangent of data is opposite over the adjacent. And then just take the arc tangent of both sides and you get to the with our tangent installation and then putting these numbers we had before in we get that the net direction is 58 degrees north of the east.

Zulfiqar Ali · Answer

well, we have the linebackers mess m A that is equal to 110 kilogram. And also we have halfbacks, mace and be well and A is equal to 85 85 kilogram and late plus X uh, access be Easton plus y X is be north, right? Eso we have I&#x27;ll be a one X is equal to zero. We a one lie is equal to 8.28 meter per second and we be one X is equal to seven point two meters per second and we be one. Why is equal to zero? Well, we need to find openly gay too, right? And then we be to well for and isolated system The total momentum before the collision equals the total momentum after the collision. So be one is equal to be to and for two particles. When this can be returnees, be a one less B B one is equal to I&#x27;ll be a do bliss be, uh, be too right and we know that momentum is given by momentum is given by mass terms lost E where momentum is equal to mass times velocity and therefore we can write the collision equipment in the following form M a dime&#x27;s we a want lis MB times we be one is equal to mm Hey, times we to less MB times we be too Well, let&#x27;s call this equation Number one Well, for two dimensional motion. Uh, this equation becomes m eight times We ate one x pless MB times Ah, we be one x that is equal to M eight times we two x lous MB times we be two x Well, let&#x27;s call this equation to a and for why direction we have m a times we a one Why jobless em be times we be one? Why and that is equal to m a times we to why we two white bliss m v times we be to lie And let&#x27;s call this encourage him to be right. And now we do calculations Well, since the field is very muddy and the forces that line baker and 1/2 bake are exerting on each other is very large. Then we considered the external metal his own Divorce on the system is approximately zero and so the momentum is conserved Also since the two players move together immediately after the collision So they have the same final velocity and therefore we have Ah, we A two x is equal to ah, we be to acts that is equal to we two x and also we a do why is equal to we be to why right? And that is able to we to why, okay and no lives, um lugging values in equation to a right. Then we have 110 into zero less 85 85 into 7.2. Well, that is equal to 110 times. Are we too explicit? 85 uh times we two x and solving for re two acts will be to excess equal to three point 14 meters per second. And also we substitute values in equation Toby. Then we have 100 in 10 into eight point it less 85 in 20 Well, that is a call to 110 times We do. I ah bless 85 times We do, I write and we too. Why we do. I is equal to 4.96 Me too. Per second, right? No, let&#x27;s find out. We well these route We two x all square bliss we to Why square? And that is equal to Route 3.14 square less ah, 4.96 clear, and that uses five point 87 meters per second. Now let&#x27;s find a Peter. When Peter is equal to gain in worse into 4.96 divided by 3.14 that is equal to 57 point seven degrees.

Ryan Williams · Answer

So here we have a schematic of our problem, where we have one player with any faction against a mass moving at a certain velocity, chasing another player, a smaller velocity there allegedly when they collide, they will act as one object with a mass of each of their messes individually, some moving at some final velocity which we want to calculate. And do you? This was gonna simply use the conservation of momentum which says that the initial momentum asked equals final momentum of the system. Well, this is our initial and this is our final situation. So our initial momentum will be the mass of the first player, plus the mass of the second player for the momentum of both players. So m one a one plus m two g two you should be the mass of the first player is 85 kilograms and his velocity, where their velocity is 5.5 meters per second and when these two are multiplied together, you&#x27;ll get the units of kilograms meters per second plus the mass of the second. She&#x27;s 95 times their velocity, which is 4.1 meters per second, adding these together plug amusing calculator will give 857 kilograms meters per second and all this fast equals the final momentum which will be the mass of both players times the velocity of both players asked equal the final for the initial momentum. 857 kilogram meters per second. If we&#x27;re solving for people&#x27;s well, give us 857 divided by the mass of both which would be 85 kilograms plus in 95 kilograms. And since the units of the But and the Dominator be kilograms, it would just be left with meters per second and plugging this again into a calculator gives approximately 4.76 Neither is per second.

João Gabriel Alencar Caribé · Answer

we saw this question by using moment in preservation. The total momentum before the collision is because they&#x27;re total momentum after the collision. Know that after the collision they stick together and not dressed for after the collision. The momentum is the cost zero because the momentum remembers proportional to p Times V. So if the is equal to zero, then the moment will cost 202 before the momentum before the collision. Waas zero already but the momentum before the collision has two contributions one from player one and another from player to true. For the first player, we have m one 31 divided by the correction factor one minus the one divided by C Square, plus the second players momentum and to the two divided by the square. Root off one miner&#x27;s V two divided by C square on the course to zero. Because off the conservation of momentum, now we have to blink in the vials that were given in the problem. So em one is close to 88. The one is because two plus two meters by second letter say that, and this is divided by the square root off one minus two divided by three Because the problem tells us pose. That seat is close to three meters by second squared plus m too, which is 120 kilograms times. Me too, which is not no divided by the square root off one miners be too divided by a squared in. These is close to zero. Now we have to solve this wall problem or be true to simplify your solution. Let us call this war term you won then 120 not plus it will be minus because we too will negative note that one player is going to the right and another one is going to the left. So 120 times be true. Divided by the square root or phone miners v choose divided by the square. He&#x27;s a ghost to be want. We begin my squaring both sides of the equation to get the following 120 squared virtual square divided by one minus ritual divided by see where it goes to be one squared. No, we continue by doing the following saying this term to the other side. 120 square kinds of each square is equal to be one square minus you One squared times the true divided by C squared. No, we&#x27;re saying this term to the other side. So 120 square V two square into coastal Be one squared. Uh, forgot your order term. So these plus few one squared V two divided by C squared is equal to P one square. So we have we have since just this term to the side of the equation. Now we can write it as v Chu Square times 120 square plus be one squared, divided by seas where you close to be one square Then we can stand this term to the other side To get reach you squared is equals to be one squared divided by 120 squared plus be one divided by sea squared Now take the square it off both sides to get me to as being close to be one divided by the square root off 120 squared close be one divided by sea Where now we have to plug in the values that we had before Now let us remember what waas be one The one was equals two 18 kinds. True, Divided by the square root off one miners. Two words square. These is approximately 236.129 kilograms meters per second. Then the two he&#x27;s equals. Two 236 0.129 divided by the square of off 120 plus 236 0.129 divided by tree square, which is approximately one 0.6 meters by second. But remember that this player is going to the left.

Sarah Mccrumb · Answer

ready is that we have a full bath moving east. And so he&#x27;s is this way, and it&#x27;s tackled and is going back. Wes backwards. Basically. So the first question is asking us to find at the blast final velocity here, and we can simply with the religion. And we have 88 kilograms here of the fullback times the velocity here. Good. I need this. Here we go. Not that. There we go, and we&#x27;re gonna be subtracting. That&#x27;s because the other guy is going ease. So we got 97 can kilograms times three meters for a second and a final velocity. They&#x27;re gonna have the same. So be up here and we&#x27;re just gonna be adding there. Um, wait there. Week together. Here we go. And I&#x27;m just gonna solve this year and we end up with for 40. And I&#x27;m actually what I&#x27;m gonna do is eliminate all these programs here so I don&#x27;t have to write it. Yeah, there we go. Minus It&#x27;s you 91. Get me up. And now would from the add those together on get 88 plus 97 one 85. And we&#x27;re just gonna Saul, and we end up with a via that is zero point eats Oh, five or 81 meeting. Well, Dr my hands. So I apologize. So here we go. And I was No, the kinetic energy. So this is just This is a really easy area, and you&#x27;re just gonna be doing, um And since the answer here is gonna be negative to, um so that you know that because your guy is going backwards. We have five squared. It was 25 waas one have 97. Okay. And of caffeine, 1/2 1 85 And then our velocity is actually this eat one. It&#x27;s quick again. I&#x27;m not using units at the moment. I&#x27;m just cause it&#x27;s easier to write all these numbers out without used in units. But you at home, you know, don&#x27;t forget what units are if you have trouble with unit&#x27;s, always include units. And here we&#x27;re just gonna solve for this part right here. We get 88 times 25 divided by two, and we end up with 11 You here, as this is answer is going to be negative. We can actually reverse the, um we can actually we&#x27;ve bursts plus hear anything? Actually, yeah. 97 times nine divided by two You get because all right, I don&#x27;t know why that became ST That&#x27;s by And here we&#x27;re gonna dio 1 85 times point eat one squared, divided by two and that we get Here we go and what it&#x27;s gonna dio. And then we&#x27;re gonna be getting *** dio one for seven by point e one and that&#x27;s our answer.

Problem

. A $\mathrm{A} 5.00$ g bullet is fired horizonta…

Problem 24 Medium Difficulty

Answer

$v_{2}=5.87 \mathrm{m} / \mathrm{s}, 57.7^{\circ}$ north of east

Related Courses

College Physics

Related Topics

Discussion

Top Physics 101 Mechanics Educators

Liev B.

Aspen F.

Jared E.

Meghan M.

Physics 101 Mechanics Courses

Math Review - Intro

Algebra - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 8

Video Transcript

Hugh D. Young

College Physics

Liev B.

Aspen F.

Jared E.

Meghan M.

Math Review - Intro

Algebra - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$v_{2}=5.87 \mathrm{m} / \mathrm{s}, 57.7^{\circ}$ north of east

College Physics

Liev B.

Aspen F.

Jared E.

Meghan M.

Math Review - Intro

Algebra - Example 1

Hugh D. YoungCollege Physics

Liev B.

Aspen F.

Jared E.

Meghan M.

Hugh D. Young

College Physics