Mathematics 9709 · AS & A Level · Discrete random variables

Discrete random variables — practice question

Particle $P$ has mass $0.2\,\text{kg}$ and is fastened to one end of a light inextensible string of length $0.6\,\text{m}$. The free end of that string is fixed at point $A$. $P$ is also attached to one end of a second light inextensible string of length $0.6\,\text{m}$, and the other end is fixed at point $B$ directly below. The particle travels in a horizontal circle of radius $0.3\,\text{m}$, centred at the midpoint of $AB$, with both strings remaining straight (see diagram).
(i)[4]

Calculate the smallest possible angular speed of $P$.

(ii)[5]

Find the maximum possible speed of $P$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate resolution $\cos \theta = 0.5$, $\sin \theta = \frac{\sqrt{3}}{2}$

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