Work and Energy Legacy Problem #12 Guided Solution

A good problem solver reads a problem carefully, identifying known and unknown information, and then plots out a strategy using physics principles and math relationships in order to get from the known information to the unknown information. Here we read of a skydiver who is traveling with a known speed at a known altitude or height above the ground, and we're asked to calculate the K.E., the P.E., and the total mechanical energy that the skydiver possesses. The M, or mass, of the skydiver is 78 kilograms. The speed at which the skydiver moves is 62 meters per second, that's the V, and the H, or height above the ground, is 870 meters. Now we're asked to calculate the K.E., and we understand K.E. to simply be the one-half times the mass times the speed squared. So we need to feed into that equation 78 for M and 62 for V. And when we do, we get 149,916 joules. We can round that to two significant digits, so we'd have 1.5 times 10 to the 5th joules. We understand the potential energy, P.E., to be equal to the product of M times G times H. So we need to take 78 again and plug it in for M. We need to use 9.8 newtons per kilogram for G. And we need to plug in 870 meters for H. When we do and perform our calculations, we get 665,028 joules. Again, we can round that to two significant digits, such that we get 6.7 times 10 to the 5th joules. Now in Part C, we're asked to determine the total mechanical energy possessed by the skydiver. When we ask total mechanical energy, we're asking the sum of all the forms of mechanical energy. And here, there's the kinetic and the potential form. So finding the total of these two forms would simply amount to adding them together. When we do, we get 814,944 joules. We'll round that to two significant digits, such that the answer is 8.1 times 10 to the 5th joules.