Momentum, Collisions and Explosions Legacy Problem #13 Guided Solution

A good problem solver has a habit of reading a problem carefully and getting a visual picture of what's going on, then identifying known and unknown quantities and plotting a strategy to get from the known quantities to the unknown quantities. The strategy plotting phase requires that a student understand some conceptual information about the physics of the situation. Here we have a picture of a male and a female skater skating forward on the ice. We're told the original speed of the male and female skater is 7.4 meters per second. They're preparing for a throw jump maneuver in which the male tosses the female forward. After the toss, the female skater is moving forward with a speed of 8.6 meters per second. She is sped up. She was going 7.4 and is now going 8.6 meters per second. Her gain in momentum should be accompanied by a loss in momentum on the male skater. We're asked to determine the speed of the male skater after the throw. And the way we'll do that is we'll use the idea that the momentum change of the female equals the same momentum change of the male, only the female gains the momentum and the male loses it. We'll use this principle to calculate the change in velocity of the male skater and then use the change to find the final speed. That's our strategy. So as we go about this, we're going to begin by calculating the momentum change of the female. Her mass is 48 kilograms, and to get the momentum change, we'll have to multiply that mass by the delta V, the change in velocity of the female. The change in the velocity of the female is 1.2 meters per second. It changed from 7.4 to 8.6. So when we multiply 48 by 1.2, we get a change in momentum of 57.6 kilograms times a meter per second. This positive 57.6 kilograms meter per second change in momentum of the female should be equivalent to a negative 57.6 change in momentum of the male. We can use this change in momentum now for the male to determine the delta V of the male as a result of this throw jump. So when we do that, we take the 57.6 and we set it equal to 82 kilograms times the delta V of the male, and we solve for the delta V of the male, which comes out to be about 0.7 meters per second, and it's a negative, indicating that the male has slowed down. Originally the male was moving at 7.4 meters per second, and after the throw jump maneuver is now moving 0.7 meters per second slower, or 6.7 meters per second.