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Question Number 20411 by Tinkutara last updated on 26/Aug/17

$$\mathrm{A}\mathrm{stone}\mathrm{of}\mathrm{weight}W\mathrm{is}\mathrm{thrown}\mathrm{straight}$$$$\mathrm{up}\mathrm{from}\mathrm{the}\mathrm{ground}\mathrm{with}\mathrm{an}\mathrm{initial}$$$$\mathrm{speed}u.\mathrm{if}\mathrm{a}\mathrm{drag}\mathrm{force}\mathrm{of}\mathrm{constant}$$$$\mathrm{magnitude}f\mathrm{acts}\mathrm{on}\mathrm{the}\mathrm{stone}\mathrm{through}$$$$\mathrm{out}\mathrm{its}\mathrm{flight},\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{stone}\mathrm{just}$$$$\mathrm{before}\mathrm{reaching}\mathrm{the}\mathrm{ground}\mathrm{is}$$

Answered by ajfour last updated on 26/Aug/17

$$0=u^2-2\left(\frac{W+f}{W}\right)gh\left(forupwardtrip\right)$$$$v^2=2\left(\frac{W-f}{W}\right)gh\left(fordownwardtrip\right)$$$$\Rightarrow \left(\frac{W-f}{W}\right)\left(u^2\right)\left(\frac{W}{W+f}\right)$$$$\Rightarrow \mathit{v}=\mathit{u}\sqrt{\frac{\mathit{W}-\mathit{f}}{\mathit{W}+\mathit{f}}}.$$

Commented by Tinkutara last updated on 26/Aug/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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