A-LevelMathematicsMechanics9709/42 · Feb/Mar 2018 · Q35 Marks

A girl, of mass 40 kg, slides down a slide in a water park. The girl starts at the point A and slides to the point B which is 7.2 metres vertically below the level of A, as shown in the diagram. [Figure 3.1]

(i)Given that the slide is smooth and that the girl starts from rest at A, find the speed of the girl at B.[2]
(ii)It is given instead that the slide is rough. On one occasion the girl starts from rest at A and reaches B with a speed of 10 m s¯¹. On another occasion the girl is pushed from A with an initial speed V m s¯¹ and reaches B with speed 11 m s¯¹. Given that the work done against friction is the same on both occasions, find V.[3]

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Mark scheme

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

(i) [M1] Use of KE gain = PE loss: 1/2 × 40 × v² = 40 × g × 7.2
(i) [A1] v = 12 m s⁻¹
(ii) [M1] Work done against friction (WDF) can be calculated as Loss in PE - Gain in KE (e.g., 40 × g × 7.2 − 1/2 × 40 × 10² = 880 J)
(ii) [M1] For 4-term work-energy equation with numerical attempt at WDF, or using the fact that WDF is the same in both cases (e.g., 1/2 × 40 × V² + 40 × g × 7.2 - WDF = 1/2 × 40 × 11² OR 1/2 × 40 × V² = 1/2 × 40 × 11² - 1/2 × 40 × 10²)
(ii) [A1] V = √21 = 4.58

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