A-LevelMathematicsMechanics9709/41 · May/June 2021 · Q36 Marks

Three particles P, Q and R, of masses 0.1 kg, 0.2 kg and 0.5 kg respectively, are at rest in a straight line on a smooth horizontal plane. Particle P is projected towards Q at a speed of 5 ms⁻¹. After P and Q collide, P rebounds with speed 1 m s⁻¹. Q now collides with R. Immediately after the collision with Q, R begins to move with speed V ms⁻¹.

(a)Find the speed of Q immediately after the collision with P.[3]
(b)Given that there is no subsequent collision between P and Q, find the greatest possible value of V.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[M1] Use of conservation of momentum, 3 terms Correct dimensions
[A1] 0.1×5+0=0.1×(-1)+0.2×(±v)
[A1] v=3 ms⁻¹ A0 for v = -3
[M1] 0.2xtheir3+0=0.2×u+0.5V Use of conservation of momentum, 3 terms, correct dimensions. Allow u = 0 used or if Q and R coalesce
[B1] u≥-1 Allow u = −1. Allow equality for finding greatest value of V. Condition for no collision with P, may be a statement.
[A1] Greatest V =1.6 FT on their 3 from 3(a) if u = −1 used.

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.