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A-LevelMathematicsMechanics9709/51 · Oct/Nov 2019 · Q47 Marks

A small ball B is projected with speed 30 m s¯¹ at an angle of 60° above the horizontal from a point O. At time t s after projection the horizontal and vertically upwards displacements of B from O are x m and y m respectively.

  1. (i)Express x and y in terms of t and hence find the equation of the trajectory of the ball.[4]
  2. (ii)Find the value of x for which OB makes an angle of 45° above the horizontal.[3]

Mark scheme

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

  1. [B1] Use horizontal motion
  2. [B1] Use s = ut + gt²/2 vertically
  3. [M1] Attempt to eliminate t
  4. [A1] y = 1.73x - 0.0222x² or y = √3x - x²/45
  5. [M1] x = y or tan 45 = y/x
  6. [M1] x common to all three terms
  7. [A1] x = 32.9

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About this question

Topic
Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 5 Variant 1, question 4.

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