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Can someone please help me to figure out how to use the 5J of energy into my equation for the maximum height. I know that the maximum height is given by,

$$h_{max}={(v_f-v_i)^2 \over 2g}$$ but I'm not sure how to factor in the air drag in Joules. My question is a basic rock with mass $m$ being thrown up vertically with a $v_i$ and to find the vertical height maximum it reaches.

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closed as off-topic by Brandon Enright, Danu, JamalS, Neuneck, Kyle Kanos Oct 6 '14 at 11:21

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I guess the $5$ joules means over the course of its entire trip. So the rock will lose $2.5$ joules on its way up. Then the gravitational potential energy at the top of its trajectory minus the $2.5$ joules should be equal to what other energy term?

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