CAIE A-Level Mathematics 4.3.2 Conservation of Linear Momentum

CAIE A-Level Mathematics 4.3.2 Conservation of Linear Momentum
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise modelling direct impacts by conserving signed linear momentum, finding post-collision velocities or shared coalesced speed and then calculating kinetic-energy loss or…

How this is tested

  • write total Σmv before impact = total Σmv after impact using one consistent positive direction
  • use one common velocity after impact when particles coalesce and separate velocities otherwise
  • combine momentum results with kinetic-energy or no-further-collision conditions to find bounds

Question 2(a)

[Maximum number: 3]

Two particles, P and Q, of masses 3 kg and 5 kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4 ms−14 \mathrm{~ms}^{-1} directly towards Q. After P and Q collide, P has speed 1 ms−11 \mathrm{~ms}^{-1}.

Find the two possible speeds of Q after the collision.