$1.07 \textrm{ m/s}$

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This is College Physics Answers with Shaun Dychko. This performer is on frictionless roller skates and initially at rest, so <i>v two</i> equals zero. The performer's mass <i>m two</i> is 65 kilograms and a cannonball is approaching them with a horizontal velocity of eight meters per second. The cannonball has a mass of ten kilograms. The performer will catch the ball and then the two things, the ball and performer combined, will move with some velocity <i>v prime</i> after the collision. So the total momentum before the collision which is the momentum of the cannonball plus the momentum of the performer, will equal the total momentum afterwards and that will be the combined mass of the two things that are stuck together, multiplied by their common velocity <i>v prime</i>. Now since the performer initially has no velocity, that means they have no momentum so this term is zero. We can divide both sides by <i>m one</i> plus <i>m two</i> and then switch the sides around so that we have the unknown on the left. So we solve for <i>v prime</i> is <i>m one v one</i> over <i>m one</i> plus <i>m two</i>. So this is ten kilograms times eight meters per second divided by ten plus 65 kilograms, giving us a velocity after the performer catches the ball, of 1.07 meters per second.