Two rigid rods $OA$ and $OB$, of lengths $5\text{ m}$ and $8\text{ m}$ respectively, are joi

Question

Two rigid rods $OA$ and $OB$, of lengths $5\text{ m}$ and $8\text{ m}$ respectively, are joined at $O$. The angle $\angle AOB=\theta$ is increasing at a constant rate of $0.14\text{ rad s}^{-1}$. At time $t$ seconds, $AB=x\text{ m}$ and the area of triangle $AOB$ is $K\text{ m}^2$. At the instant when $\theta=\frac{\pi}{3}$, find the rate at which $x$ is increasing;[3] the rate at which $K$ is increasing.[2]

Accepted Answer

(i) $\frac{2\sqrt{3}}{5}\text{ m s}^{-1}$ (ii) $\frac{7}{5}\text{ m}^2\text{ s}^{-1}$

Changing separation and area of two hinged rods

Changing separation and area of two hinged rods

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