Problem involving Bearing

Problem involving Bearing

Secondary 3

Two ships \(A\) and \(B\) leave a port \(P\) at \(0915\) hour.
Ship \(A\) sails on a bearing of \(120{}^\circ\) at \(25\) km/h for an hour and stops at \(X\).
Ship \(B\) sails on a bearing of \(160{}^\circ\) at \(40\) km/h for an hour and stops at \(Y\).

  1. After an hour, find the
    1. distance between ships \(A\) and \(B\).
    2. bearing of ship \(A\) from ship \(B\).
    3. Find how far is ship \(B\) due east of port \(P\).
  2. If ship \(B\) anchored at point \(Y\) after an hour whereas ship \(A\) continues its sail, find the shortest distance between ship \(A\) and ship \(B\).
  3. If ships \(A\) and \(B\), after an hour, then travel towards each other with their speeds unchanged, when will they meet?

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Answer:(a)(i) \(26.3\text{ km}\text{ (3 s.f.)}\) (ii) \(017.6^\circ\text{ (1 d.p.)}\) (iii) \(13.7\text{ km}\text{ (3 s.f.)}\) (b) \(25.7\text{ km}\text{ (3 s.f.)}\) (c) \(1039\text{ hours}\)

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