# Conservation of Energy confusion

**1. The problem statement, all variables and given/known data**

A dog takes a running horizontal leap off a 10 m cliff and jumps with a speed of 3 m/s onto a ledge 4 m below the height of the cliff. With what speed does he land on the ledge?

**2. Relevant equations**

KE_{i} + PE_{i} = KE_{f} + PE_{f}

1/2mv_{i}^{2} + mgh_{i} = 1/2mv_{f}^{2} + mgh_{f}

**3. The attempt at a solution**

Attempt #1:

(masses cancel, g ≈ 10m/s^{2})

1/2(3m/s)^{2} + (10m/s^{2})(10m) = 1/2v_{f}^{2} + (10m/s^{2})(4m)

1/2(9)+100 = 1/2v_{f}^{2} + 40

4.5 + 60 = 1/2v_{f}^{2}

2(64.5) = 129 = v_{f}^{2}

[itex]\sqrt{}129[/itex] = v_{f}

v_{f} = 11.36

This is not the correct answer, however, upon looking at the solution the only difference is that they make the original height equal to zero and the final height equal to -4. This of course excludes PE from the first half of the equation. I realize that it would have been simpler for me to do the problem in that way. I don’t, however, understand why it doesn’t work to do it the way that I did it. Shouldn’t it only be the difference in PE that matters? Should the final height have been something different than 4 for my version to work? Any clarification would be greatly appreciated.

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