Question

prove that the total energy of a free falling body is conserve please ​

Answer 1

$let \: the \: energy \: of \: particle \: at \: any \\ height = e \\ initial \: energy = \frac{1}{2} m {v}^{2} + mgh \\ = 0 + mgh \\ = e0 \\ velocity \: at \: any \: height = v \\ {v}^{2} = {u}^{2} + 2as \\ {v}^{2} = 0 + 2( - g)( - (h - d)) \\ = 2g(h - d) \\ e = \frac{1}{2} m {v}^{2} + mgd \\ = \frac{m}{2} .2gd(h - d) + mgd \\ = mgh \\ = e0 \\ \\ || hence \: constant ||$

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