A-LevelMathematicsMechanics9709/52 · Feb/Mar 2018 · Q13 Marks

A uniform rectangular block has a square base ABCD with AB = BC = 0.4 m. The height of the block is h m. The block is placed with its base on a rough plane inclined at 30° to the horizontal. The block does not slide. It is given that the block is on the point of toppling when the diagonal AC lies along a line of greatest slope. Calculate h.

A uniform rectangular block has a square base ABCD with AB = BC = 0.4 m. The height of the block is h m. The block is placed with its base on a rough plane inclined at 30° to the horizontal. The block does not slide. It is given that the block is on the point of toppling when the diagonal AC lies along a line of greatest slope. Calculate h.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

[B1] d = √(0.2²+ 0.22) (= 0.2828) OR AC = √(0.42 +0.4²) (= 0.56568..) Note d = ½ AC
[M1] tan30 = 0.2828 / (h / 2)
[A1] h = 0.98(0) 2√6/5

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source: A-Level Mathematics, Feb/Mar 2018 Paper 5 Variant 2, question 1.

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