Figures shows a mass M attached to the middle of string, the two ends of which are passing over two

Question

Figures shows a mass M attached to the middle of string, the two ends of which are passing over two pulleys $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$. To the ends of strings are attached masses $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$ . If the two parts of the string attached to M are inclined at an angle $2 	heta$ and the instantaneous downward velocity of the masses $M_{1}$ and $M_{2}$ is $v$, what is the upward velocity of M\

Professor PC Thomas Classes · Answer

$$ \begin{equation*} \mathrm{v}=\frac{\mathrm{dy}}{\mathrm{dt}} 	ag{1} \end{equation*}$$ $\qquad$ $$\begin{equation*} \mathrm{v}^{\prime}=\frac{\mathrm{dx}}{\mathrm{dt}} 	ag{2} \end{equation*}$$ $\mathrm{a}=$ constant\ $x^{2}+a^{2}=y^{2}$. Differentiating with respect to $t$\ $2 x \frac{d x}{d t}+0=2 y \frac{d y}{d t}$\ $x v^{1}=y v \quad v^{1}=\left(\frac{y}{x}ight) v=\frac{v}{\frac{x}{y}}=\frac{v}{\cos 	heta}$\