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Question Number 23548 by ajfour last updated on 01/Nov/17

Commented by ajfour last updated on 01/Nov/17

$$Find\mathit{v}intermsof\mathit{u},\mathit{a},\mathit{b},and\mathit{l}$$$$atamomentwhenthecollars$$$$atdistances\mathit{a},and\mathit{b}fromthe$$$$verticalrodofthestand.$$

Commented by mrW1 last updated on 01/Nov/17

$$\mathrm{let}\mathrm{h}=\mathrm{distance}\mathrm{of}\mathrm{the}\mathrm{horizontal}\mathrm{rods}$$$${\mathrm{L}}^2={\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{h}}^2$$$$\mathrm{L},\mathrm{h}=\mathrm{constant}$$$$\mathrm{differentiate}\mathrm{w}.\mathrm{r}.\mathrm{t}.\mathrm{time}$$$$0=2\mathrm{a}\frac{\mathrm{da}}{\mathrm{dt}}+2\mathrm{b}\frac{\mathrm{db}}{\mathrm{dt}}+0$$$$0=2\mathrm{au}+2\mathrm{b}(-\mathrm{v})+0$$$$\Rightarrow \mathrm{v}=\frac{\mathrm{a}}{\mathrm{b}}\times \mathrm{u}$$

Commented by ajfour last updated on 01/Nov/17

$$\mathcal{E}xcellentsir!Iliketheproperty$$$$toowell.$$

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