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A-LevelMathematicsMechanics9709/53 · May/June 2018 · Q49 Marks

A small object is projected from a point O with speed V m s⁻¹ at an angle of 45° above the horizontal. At time t s after projection, the horizontal and vertically upwards displacements of the object 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 path.[4]
  2. (ii)The object passes through the point with coordinates (24, 18). Find V.[2]
  3. (iii)The object passes through two points which are 22.5 m above the level of O. Find the values of x for these points.[3]

Mark scheme

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

  1. [B1] x = (Vcos45)t
  2. [B1] y = (Vsin45)t - gt²/2
  3. [M1] Attempt to eliminate t
  4. [A1] y = x - 10x² / V²
  5. [M1] Substitutes x = 24, y = 18 in part (i) equation
  6. [A1] V = 31(.0)
  7. [M1] Put y = 22.5 in part (i)
  8. [M1] x² - 96x + 2160 = 0
  9. [A1] x = 36, 60

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About this question

Topic
Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.
Source
A-Level Mathematics, May/June 2018 Paper 5 Variant 3, question 4.

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