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Two ice skaters, Daniel (mass 65.0 $\mathrm{kg}$ ) and Rebeca (mass 45.0 $\mathrm{kg}$ , are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.0 $\mathrm{m} / \mathrm{s}$ before she collides with him. After the collision, Rebecca has a velocity ofmagnitude 8.00 $\mathrm{m} / \mathrm{s}$ at an angle of $53.1^{\circ} \mathrm{from}$ her initial direction. Both skaters move on the frictionless, horizontal surface of the rink. (a) What are the magnitude and direction of Daniel's velocity after the collision? (b) What is the change in total kinetic energy of the two skaters as a result of the collision?

(a) $v_{D 2}=7.20 \mathrm{m} / \mathrm{s}, 38.0^{\circ}$ below $+x$ -axis(b) $\Delta K=-678.5 \mathrm{J}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

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here in this question we have given moss oh person one That is M1 equals two 65 kg. Moss of person oh That is M2 equal to 45 K. Z. Also speed before or laser against. You want a quarter to zero and you two equal to 13 meter per second and steve after. Well listen here we have the speed of second person that is we do equal to eight meta for a second. And also we have the value of teeter equal you The P 3.1 Living. Now we have to find out the magnitude of velocity and direction of daniel after collision. And then we have to calculate the change in total kinetic energy. So here we know that according to law of conservation of momentum. If X and Y component of total momentum. So it gives and one U one X plus I am too you two X equal to M one V 1 x less. I am too need to X. Now we considered it as equation one and similarly anyone you want why less? I am too you do why equals two. And when we went by less I am too we do. Why now we consider this as equation two. Now here we assume that the speed and direction of the person one after coalition. We we will and peter respectively. So we have New one x equal to you want right equal to zero. New two X equal to 13 m/s. You too. Life it will do zero we want X equal to we want cause cheetah and we wonder why equal to we will sign tita and we two X equal to eight cause 53 on one degree. Also we too why? Equal to eight signs 53.1 dignity which is equal to six point four m per second. And the two X. Is actually equal to 4.8 tomato per second. The now when we're putting these In the equation one and equation two we have we run X equal to mm to multiply by You two X-. Need to X. Yeah I did buy m one. Now we substitute the values so we get to be even X equal to 45 multiplied by 13 minus 4.8 divided by 65. So we get we want x equal to 5.7 m/s. Now. Similarly we want Why from equation too Can be written as -12 divided by and one multiply by V. Two. Why now here on putting the values we get even why equals two minus 45 divided by 65. multiplied by 6.4. So We get we even why equals 2 -2 4.43 m/s. Now we are going to find the magnitude of velocity for daniel and then find the direction also. So here in party magnitude of velocity is given by driven equal to the square root of we even X. Square plus we world why square now I'm putting the values we get. We even equal to scrabble off 5.7. Holy Square plus -4.3 Whole Square. So we get We one equals 2 7.2 m/s. So this is the magnitude of fellow city for Daniel after the call is um now we find that direction so direction. Can we find out by using the expression tita equal to and the universe we run. Why divided by we want X. So we got t type well to 10 in reverse -4.48 divided by 5.7. So he got Theta is equal to 38 daily. So here Negative sign shows that the direction is 38, three below the or is it ex excess No comes to part B. So here we are going to find out the change in total kinetic energy. So sands and daughter by native energy is then E equals two. one divided by two. Anyone we want square plus one divided by two. I am too. We two squared minus one divided by two. Anyone you won a square Plus one divided by two and you do square. So yeah, by simply fine. A bow. We get the L K E equals to one divided by two. Multiply by emblems. We went square less. I am too the two scraps minus M one New one is where now here As you two equals to zero. Therefore this becomes zero. So now we substitute the values of M and given em to veto and M and human. In the equation we get Dell E Equals to one divided by two 80/h by 65. Multiply by 7.2. Holy scratch less 45. multiplied by a holy square minus 45. multiplied by 13 whole square. So from a bow we get Bell e equals two minus 67 mm june. The change in total kinetic energy equals 2 -678 jewels.

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