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<p>The diagram shows a mechanism for converting rotational motion into linear motion. The point $P$ is on the circumference of a disc of fixed radius r which can rotate about a fixed point $O$. The point $Q$ can only move on the line $OX$, and $P$ and $Q$ are connected by a rod of length $2r$. As the disc rotates, the point $Q$ is made to slide along $OX$. At time t, angle $POQ$ is $\theta$ and the distance $OQ$ is $x$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">State the maximum and minimum values of $x$.</span></div><p style="text-align: right;">[1]</p></li><li><div class="list-item-content"><span class="list-item-text">Show that $x=r\left( \cos \theta +\sqrt{4-{{\sin }^{2}}\theta } \right)$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">At a particular instant, $\theta =\frac{\pi }{6}$ and $\frac{\mathrm{d}\theta }{\mathrm{d}t}=0.3$. Find the numerical rate at which point $Q$ is moving towards point $O$ at that instant, leaving your answer in terms of $r$.</span></div><p style="text-align: right;">[3]</p></li></ol>

The diagram shows a mechanism for converting rotational motion into linear motion. The point $P$ is on the circumference of a disc of fixed radius r which can rotate about a fixed point $O$. The point $Q$ can only move on the line $OX$, and $P$ and $Q$ are connected by a rod of length $2r$. As the disc rotates, the point $Q$ is made to slide along $OX$. At time t, angle $POQ$ is $\theta$ and the distance $OQ$ is $x$.

State the maximum and minimum values of $x$.

Show that $x=r\left( \cos \theta +\sqrt{4-{{\sin }^{2}}\theta } \right)$.

At a particular instant, $\theta =\frac{\pi }{6}$ and $\frac{\mathrm{d}\theta }{\mathrm{d}t}=0.3$. Find the numerical rate at which point $Q$ is moving towards point $O$ at that instant, leaving your answer in terms of $r$.

2019 EJC P2 Q2

2019 EJC P2 Q2

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