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0606/21 Oct/Nov 2025, Question 12: Velocity Vectors and Moving Objects

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Two boats move at constant velocity from different starting points and times; find their velocity vectors and demonstrate that their paths meet.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Express each boat's velocity as a vector in metres per second, using east and north components.

  1. 1Bearing 030° is 60° above east: v_A = (5√3 cos 60°, 5√3 sin 60°) = (5√3/2, 15/2)
  2. 2Bearing 060° is 30° above east: v_B = (10 cos 30°, 10 sin 30°) = (5√3, 5)

AnswerA: column vector (5√3/2, 15/2); B: column vector (5√3, 5)

Part (b) · 5 marks

Using the given start times and positions, show that the two boats occupy the same position simultaneously.

  1. 1Position of A at time t: t(5√3/2, 15/2)
  2. 2Position of B at time t (t ≥ 100): (0, 1000) + (t − 100)(5√3, 5)
  3. 3East: (5√3/2)t = 5√3(t − 100) gives t = 200
  4. 4North: (15/2)t = 1000 + 5(t − 100) gives (5/2)t = 500, t = 200
  5. 5Both components give the same time t = 200, so the boats are at the same point then: they collide

AnswerBoth components agree at t = 200 s (100 s after B starts), so the boats collide

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