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Giancoli 6th Edition, Chapter 6, Problem 36


Chapter 6, Problem 36 is solved.

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Transcript for this Giancoli solution

We know that the size of the change in kinetic energy is going to be, the same as the size of the change in this high jumpers potential energy. So then we need expressions for each of those. For the change in kinetic energy, we are going to write it as one half 'mvi' squared, minus one half 'mvf' squared. That's a little unusual, normally you'd write one half 'mvf' squared, minus one half 'mvi' squared, but I'm doing it this way, because I want this left side to be positive, so that it is equal to the right side. We're dealing with everything being positive. That's what the absolute value signs are about. And, I know this will be positive because their speed at the top of the jump is less than it was initially. So this is going to end up being a positive difference. So we have to solve for the initial speed, so we'll take this term and add it to both sides, also multiply everything by 2. Cancel out the common factor 'm', and take the square root of both sides, then we'll have 'vi'. So 'vi' is the square root of 'vf' squared. No one half of it in front of it anymore, because we multiplied everything by 2, and plus 2'gh'. So we have 'vi' is the square root of 2 times 9.8 times 2.10 meters, so that was that terms' potential energy, plus the kinetic energy that they have at the top there. We're just going to use that part of it, 'vf' squared. And our answer is # meters per second.