Lemmara logoLemmaraWorked solution

0606/23 May/Jun 2025, Question 10: Velocity Vectors and Moving Objects

Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given two particles' starting position vectors and constant velocities, find each position vector at time t and decide whether the particles collide.

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

Part (a) · 3 marks

P starts at −30j and moves at 58 m s⁻¹ along 20i + 21j; find its position vector at time t.

  1. 1|20i + 21j| = √(20² + 21²) = 29
  2. 2Velocity = (58/29)(20i + 21j) = 40i + 42j
  3. 3Position vector = −30j + t(40i + 42j) = 40t i + (42t − 30)j

Answer−30j + t(40i + 42j)

Part (b) · 4 marks

Q starts at −10i + 18j with speed 75 m s⁻¹ at angle α where tan α = 7/24; find its position vector at time t.

  1. 1tan α = 7/24, so the direction is 24i + 7j
  2. 2|24i + 7j| = 25
  3. 3Velocity = (75/25)(24i + 7j) = 72i + 21j
  4. 4Position vector = −10i + 18j + t(72i + 21j) = (72t − 10)i + (21t + 18)j

Answer−10i + 18j + t(72i + 21j)

Part (c) · 2 marks

Using the position vectors from parts a and b, determine whether P and Q collide.

  1. 1i components: 40t = 72t − 10, so t = 10/32 = 5/16
  2. 2j components: 42t − 30 = 21t + 18, so t = 48/21 = 16/7
  3. 3The values of t are different, so P and Q do not collide

AnswerThey do not collide (t = 5/16 from the i components but t = 16/7 from the j components)

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: 0606/23/M/J/25 · 0606_s25_qp_23 · 0606 s25 23 · question 10.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.