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A-LevelMathematicsMechanics9709/43 · May/June 2021 · Q59 Marks

A car of mass 1400 kg is towing a trailer of mass 500 kg down a straight hill inclined at an angle of 5° to the horizontal. The car and trailer are connected by a light rigid tow-bar. At the top of the hill the speed of the car and trailer is 20 m s⁻¹ and at the bottom of the hill their speed is 30 m s⁻¹.

  1. (a)It is given that as the car and trailer descend the hill, the engine of the car does 150000 J of work, and there are no resistance forces. Find the length of the hill.[5]
  2. (b)It is given instead that there is a resistance force of 100 N on the trailer, the length of the hill is 200 m, and the acceleration of the car and trailer is constant. Find the tension in the tow-bar between the car and trailer.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [B1] May be implied by energy equation.
  2. [B1] May be implied by energy equation.
  3. [M1] For attempt at work/energy equation
  4. [A1] Correct
  5. [A1]
  6. [M1] Use of v² = u² + 2as
  7. [A1]
  8. [M1] For applying Newton's second law to the trailer.
  9. [A1]

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About this question

Topic
Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.
Source
A-Level Mathematics, May/June 2021 Paper 4 Variant 3, question 5.

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