Lemmara logoLemmaraWorked solution

0606/22 May/Jun 2026, Question 7: Velocity Vectors and Moving Objects

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using i east and j north in kilometres and hours, boat A leaves P(2i+5j) at 13 00 with velocity 8i+8j; boat B leaves Q(20i+8j) at 15 00 on bearing 300° at 5√3 km/h. Find positions and separation at 17 00.

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

Part (a) · 1 mark

Find A's position vector after sailing for 2 hours from P.

  1. 1Position = 2i + 5j + 2(8i + 8j)
  2. 2= 18i + 21j

Answer18i + 21j

Part (b) · 1 mark

State A's position vector after t hours of sailing from P.

  1. 1Position = initial position + t × velocity
  2. 2= 2i + 5j + t(8i + 8j) = (2 + 8t)i + (5 + 8t)j

Answer2i + 5j + t(8i + 8j)

Part (c) · 3 marks

Find B's position vector at 17 00 after leaving Q at 15 00 on bearing 300° at speed 5√3.

  1. 1Bearing 300° is 60° west of north
  2. 2Velocity = 5√3 sin 300° i + 5√3 cos 300° j = −7.5i + (5√3/2)j
  3. 3B sails for 2 hours (15 00 to 17 00)
  4. 4Position = 20i + 8j + 2(−7.5i + (5√3/2)j) = 5i + (8 + 5√3)j

Answer5i + (8 + 5√3)j

Part (d) · 3 marks

Find the distance between boats A and B at 17 00.

  1. 1At 17 00 A has sailed 4 hours: OA = 2i + 5j + 4(8i + 8j) = 34i + 37j
  2. 2OB = 5i + (8 + 5√3)j
  3. 3AB = 29i + (29 − 5√3)j
  4. 4Distance = √(29² + (29 − 5√3)²) = 35.4 km

Answer35.4 (35.421…)

Stuck on a step? Read the free lesson: Velocity Vectors and Moving Objects

Practise more velocity vectors and moving objects questions

Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on velocity vectors and moving objects

Also searched as: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 7.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.