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Question Number 177546 by peter frank last updated on 07/Oct/22

$$\mathrm{A}\mathrm{particle}\mathrm{is}\mathrm{projected}\mathrm{vertically}$$$$\mathrm{upward}\mathrm{in}\mathrm{a}\mathrm{constant}\mathrm{gravitation}$$$$\mathrm{field}\mathrm{with}\mathrm{initial}\mathrm{speed}\left({\mathrm{v}}_0\right).\mathrm{show}$$$$\mathrm{that}\mathrm{there}\mathrm{is}\mathrm{retarding}\mathrm{proportional}$$$$\mathrm{to}\mathrm{the}\mathrm{square}\mathrm{of}\mathrm{the}\mathrm{instantaneous}$$$$\mathrm{speed},\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{partical}$$$$\mathrm{when}\mathrm{it}\mathrm{returns}\mathrm{on}\mathrm{the}\mathrm{initial}$$$$\mathrm{position}\mathrm{is}\frac{{\mathbf{v}}_{\mathbf{o}}{\mathbf{v}}_{\mathbf{c}}}{\sqrt{{\mathbf{v}}_{\mathbf{o}}^2+{\mathbf{v}}_{\mathbf{c}}^2}}\mathbf{where}{\mathbf{v}}_{\mathbf{c}}\mathbf{i}\mathrm{s}$$$$\mathrm{terminal}\mathrm{speed}$$

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