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Two objects (A and B) of equal mass collide elastically. Mass A is initially moving 5.0 m/s in the +x-direction prior to the collision. Mass B is initially moving 3.0 m/s in the –x-direction prior to the collision. After the collision, mass A will be moving with a velocity of 3.0 m/s in the –x-direction. What will be the velocity of mass B after the collision?
  1. 3.0 m/s in the +x-direction
  2. 5.0 m/s in the +x-direction
  3. 3.0 m/s in the –x-direction
  4. 5.0 m/s in the –x-direction
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OpenStax College Physics for AP® Courses Solution, Chapter 8, Problem 31 (Test Prep for AP® Courses) (1:41)

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This is College Physics Answers with Shaun Dychko. Conservation of momentum says that mass A times velocity A plus mass B times velocity B before the collision, this total has to be the same as the total momentum after the collision, mass A <i>vA prime</i> plus <i>mB vB prime</i>. We're told that the masses are all the same so <i>mA</i> and <i>mB</i> are common factors and we can divide everything by that common factor. So we end up with <i>vA</i> plus <i>vB</i> equals <i>vA prime</i> plus <i>vB prime</i>. We can solve this for <i>vB prime</i> by subtracting <i>vA prime</i> from both sides and then switching the sides around. So the velocity of the object B after collision will be velocity A plus velocity B both before the collision, minus velocity A after collision. So before collision mass A has a positive 5.0 meters per second velocity. Mass B is moving in the negative x direction so we put in negative three meters per second and then minus the velocity of mass A after the collision. We're told that it's moving at a velocity of three in the negative x direction. So we substitute negative three meters per second in place of <i>vA prime</i>. So we have a minus three here and this is a positive three in the end after the minus sign in the equation and the negative of a number and so these make zero and we're left just with five. That's positive five and so mass B will be moving in the positive x direction with a velocity of five meters per second after the collision