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2022 ACSI EOY P2 Q5

2022 ACSI EOY P2 Q5

IP 2
11 marks

  1. The angle of depression of a ship from a cliff top was \(34^{\circ}\). As the ship sailed \(250\) m further away from the cliff, the angle of depression became \(26^{\circ}\). Find the height of the cliff.

    [5]

  2. A weight at the end of a non-elastic string of length \(50\) cm is attached to point \(O\). It swings from starting point \(X\) and stops at \(Y\), passing through the lowest point \(L\) as shown in Diagram I.

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    1. Given that the vertical height between the highest and lowest points of the \(XY\) oscillation is \(5\) cm, find the angle \(XOY\).

      [3]

    2. The weight starts from a different starting point \(A\) and ends at point \(B\) as shown in Diagram II where angle \(AOB\) is \(70^{\circ}\). Find the horizontal distance \(AB\).

      [3]
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Solution:

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Answer:(a) \(440\) m (3 s.f.), under the direct-away model. (b)(i) \(51.7^\circ\) (1 d.p.). (ii) \(57.4\) cm (3 s.f.).

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