A-LevelMathematicsMechanics9709/41 · Oct/Nov 2025 · Q66 Marks

A particle A of mass 2.5kg is released from rest from the top of a smooth plane, which makes an angle of sin⁻¹ 0.2 with the horizontal. The particle A collides 2 seconds later with a particle B, of mass 3 kg, which is moving up a line of greatest slope of the plane. The speed of B immediately before the collision is 3.5 ms⁻¹. Immediately after the collision, B has a velocity of 0.5 ms⁻¹ down the plane. Find the distance A moves up the plane after the collision.

A particle A of mass 2.5kg is released from rest from the top of a smooth plane, which makes an angle of sin⁻¹ 0.2 with the horizontal. The particle A collides 2 seconds later with a particle B, of mass 3 kg, which is moving up a line of greatest slope of the plane. The speed of B immediately before the collision is 3.5 ms⁻¹. Immediately after the collision, B has a velocity of 0.5 ms⁻¹ down the plane. Find the distance A moves up the plane after the collision.[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[B1] Acceleration of A down the plane is g×0.2[=2] Allow -g×0.2. Allow ±g×sin12 or better. Allow 2.5a = 2.5g×0.2.
[*M1] Speed of A before collision is gx0.2×2[=4] Use of v=u+at with u = 0, t = 2 and their a which must be equivalent to either ±g×sin12 or ±g×cos12 ONLY.
[DM1] 3x3.5+2.5×(-4)=3×(-0.5)+2.5xu Attempt at conservation of linear momentum; four non-zero terms – allow sign errors. M1A0 only if using weight rather than mass.
[A1] u = 0.8 Correct speed (or velocity) of A after impact.
[DM1] 0=0.8²+2x(-g×¹/₅)×s Use of v² = u² + 2as (or other complete method to find s) with v = 0, their u and their -a condone sign errors. Dependent on both previous M1 marks.
[A1] s = 0.16 m CWO.

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