A-LevelMathematicsMechanics9709/42 · Feb/Mar 2025 · Q36 Marks

An aeroplane is flying at a constant speed.

(a)The aeroplane is flying horizontally. The aeroplane's engines are producing a constant power of 5500kW, and the aeroplane experiences a constant horizontal resistance force of 25kN. Find the speed of the aeroplane.[2]
(b)The aeroplane then ascends 300m in 50s, while maintaining the same speed. The resistance force is no longer constant, and the work done against the resistance force in ascending the 300m is 270000 kJ. The mass of the aeroplane is 60000 kg. Find the average power of the aeroplane's engines.[4]

Mark scheme

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

M1 OE For use of Power = Fv. Allow errors in use of kN and/or kW.
A1
B1 180 000 kJ or 180 000 000 J.
B1 OE
M1 For work energy equation with 3 terms; Allow with work done by engines instead of Power × 50; Allow sign errors; dimensionally correct.
A1

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Feb/Mar 2025 Paper 4 Variant 2, question 3.

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