Momentum, Collisions and Explosions Legacy Problem #24 Guided Solution

A good problem solver reads the problem carefully and develops a mental picture of what's going on in the physical situation. You'll notice my effort to develop a mental picture as I've drawn a diagram of the pre- and post-collision speeds and masses of the two objects involved in this collision. A good problem solver also identifies the known and unknown information. A diagram is a great place to include this type of information. Finally, a good problem solver uses an understanding of physics principles and conceptual reasoning skills in order to plot a strategy and get from known information to unknown information. In this problem, we read about Rex, who is moving along in his bumper car at 2.05 meters per second. That's a pre-collision velocity. Rex has a mass of 86 kilograms, and we're told later that the mass of his bumper car is 125 kilograms. Together, this is 211 kilograms. He is heading towards Tex, who is at rest in his path. Tex has got an initial velocity of 0 meters per second. His mass is stated as 92 kilograms, and he's in a 125-kilogram car. This is a total mass of 217 kilograms. After the collision, we're told that Tex begins moving along at 1.40 meters per second. We're asked to determine the post-collision velocity of Rex. That's our unknown quantity. Our principle we use to get from the known to the unknown information is the principle that in a collision occurring in an isolated system, the total system momentum, that is the momentum of both objects combined, is the same before the collision as after the collision. So I can write a mathematical statement in which I equate pre-collision momentum to post-collision momentum. Doing that, I'd write this statement. The mass of Rex times the velocity of Rex before the collision, 211 times 2.05, plus the max of Tex times his velocity before the collision, 217 times 0, is equal to the mass of Rex times the velocity of Rex after the collision, which I will express as 211 times v prime, plus the mass of Tex times the velocity of Tex after the collision, 217 times 1.40. I now have a single equation with a single unknown in it, the unknown being the unknown I'm trying to solve for, the post-collision velocity of Rex. I can simplify the equation as 432.55 kilograms times a meter per second on the left side, and on the right side it becomes 211 times v, plus 303.8 kilograms meter per second. Now I'm going to subtract 303.8 kilograms meter per second from both sides of the equation so I can get the term with v prime by itself. That gives me 128.75 is equal to 211 v prime. If I divide through by 211, I'll be solving for v. The v comes out to be 0.6102. I can round that to 0.61 meters per second.