A-LevelMathematicsMechanics9709/51 · Oct/Nov 2017 · Q24 Marks

A small ball is projected from a point 1.5 m above horizontal ground. At a point 9 m above the ground the ball is travelling at 45° above the horizontal and its velocity is 4 m s⁻¹. Find the angle of projection of the ball.

A small ball is projected from a point 1.5 m above horizontal ground. At a point 9 m above the ground the ball is travelling at 45° above the horizontal and its velocity is 4 m s⁻¹. Find the angle of projection of the ball.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[B1] Vcosθ = 4cos45 Using horizontal motion with V = velocity of projection and θ = angle of projection.
[M1] (4sin45)² = (Vsinθ)² – 2g(9–1.5) (leads to Vsinθ =√158) Uses v²=u²+2as vertically.
[M1] tanθ = √158/(4cos45) Uses trigonometry.
[A1] θ = 77.3°

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2017 Paper 5 Variant 1, question 2.

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