A-LevelMathematicsMechanics9709/42 · Oct/Nov 2019 · Q57 Marks

Two particles A and B move in the same vertical line. Particle A is projected vertically upwards from the ground with speed 20m s⁻¹. One second later particle B is dropped from rest from a height of 40 m.

(i)Find the height above the ground at which the two particles collide.[4]
(ii)Find the difference in the speeds of the two particles at the instant when the collision occurs.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[B1] OE
[M1] Set up an equation using their hA, their hB and 40
[DM1] Solve for t and attempt to find the height at collision.
[A1] T = 2.5 and height at collision = 8.75 m
[M1] Use of their t or their h < 20 from 5(i) in a constant acceleration formula which would lead to finding VA
[M1] Use of their t + 1 or their 40 – h from 5(i) in a constant acceleration formula which would lead to finding VB
[A1] Difference = 10 ms⁻¹ CWO

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, Oct/Nov 2019 Paper 4 Variant 2, question 5.

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