A-LevelMathematicsMechanics9709/42 · Feb/Mar 2025 · Q57 Marks

Three particles P, Q and R, of masses 0.6kg, 0.4 kg and 0.8 kg respectively, are at rest in a straight line on a smooth horizontal plane. The distance from P to Q is 3 m, and the distance from Q to R is also 3 m (see diagram). P is projected directly towards Q with speed 3 ms⁻¹. After P and Q collide, P continues to move in the same direction with speed 1.5 ms⁻¹. [Figure X.X]

(a)Find the speed of Q after the collision.[2]
(b)In the subsequent collision between Q and R, these particles coalesce. Find the speed of the combined particle after this collision.[1]
(c)Find the time that it takes from when P is initially projected until the instant at which P collides with the combined particle.[4]

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Mark scheme

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

M1 Attempt at conservation of momentum. 3 non-zero terms. Allow sign errors.
A1 OE must be positive. Allow max M1A0 if g included with the masses.
B1FT OE condone including g if already penalised in (a). FT their 2.25.
*B1FT Q takes [3/their 2.25] s [=4/3] s to reach the point at which R was initially.
*B1FT OR 3 - [3/their 2.25] x 1.5 [=1]
DM1 Dependent on both previous B marks. For attempt to find time.
A1 Allow 3.67 s.

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