Momentum, Collisions and Explosions Legacy Problem #20 Guided Solution

A good problem solver reads the problem carefully and develops a mental picture of what's going on, identifies the known and the unknown quantities, and then uses physics principles and conceptual reasoning skills to plot out a strategy as to how to get from the known information to the unknown information. Here the picture we have is of two roller skaters who are rolling along the rink. One of them has a mass of 68 kilograms and is moving faster at 17.0 meters per second. She's approaching a second roller skater who's got a 76 kilogram mass and is moving at 12 meters per second. The 68 kilogram skater jumps on the back of the 76 kilogram skater and the two move together almost as one object after the collision with the same speed. What we're asked to determine is the speed of the objects after the collision. Now in a problem such as this you need to use a principle that goes like this. The total momentum of both objects before the collision is equal to the total momentum of both objects after the collision. The total momentum meaning the momentum of both skaters. Now we're going to find the momentum before the collision by going the mass of animosity times her velocity plus the mass of Sandra Day O'Clover times her velocity. So before the collision we would write 68 kilograms times 17 meters per second plus 76 kilograms times 12 meters per second is equal to the pre-collision momentum of the system of two objects. When you do the math for that you get 1156 plus 912 a sum of 2068 units of momentum. That's the before collision momentum of the two players. That should also be equal to the after collision momentum of the two roller derby players. So we say after the collision the momentum of animosity is 68 times her velocity and we don't know her velocity is what we're looking for. So we're just going to call it an unknown variable like x or better yet we'll call it v. And for the other roller derby player Sandra Day O'Clover her momentum is 76 times her velocity and it's the same velocity because Anna is on Sandra's back. So that velocity is defined as v. So after the collision the total momentum is 68v plus 76v together that's 144v and that's equal to the pre-collision momentum which was 2068. So if you say 2068 equals 144v and you divide through by 144 you can get the v value which ends up being 14.36 meters per second. We can round that to 14 meters per second.