Work and Energy Legacy Problem #24 Guided Solution

An effective problem solver reads the problem carefully, getting a mental picture of what's going on, recording the known quantities and the unknown quantities, and then plotting a strategy using physics ideas and math relationships to get from the known quantity to the unknown quantity. Here, the only known quantity that we have is the initial velocity of a baseball, 45.0 meters per second. We're told the baseball is thrown straight upwards, and we wish to determine the final height, the height to which it would travel relative to the release location. That is, find the hf when the vf is zero. Now, you see a five-term equation on this page, and much of the problem solving in this unit can be centered around this equation. Using the equation, we can begin to cancel some terms. For instance, initially, there's no potential energy for this ball, but there is kei, and if we can assume that air resistance is negligible, then we could say that the w and c is zero. The only work being done is being done by a conservative force, the force of gravity. On the right side of this five-term equation, we could say that kef is zero, but the pf is not. So, we've now taken a five-term equation and reduced it to a two-term equation, that equation being kei equals pef. As far as kei goes, it's going to be one-half mv45 squared, and as far as pef goes, it's going to be m times 9.8 times hf. Now, you'll notice there's an m on both sides of the equation, so we can divide through by m and cancel this m. The equation then becomes one-half times 45 squared is equal to 9.8 times h. Dividing through by 9.8, we can find the final height of the ball. It is 103 meters, about 340 feet.