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Rates of change and differential equations — Question 18

QCAA 2025, Paper 1 · 6 marks

Q18 · 2025 · Technology-freeComplex unfamiliar6 marks

QUESTION 18 (6 marks)

An object is projected at an acute angle of θ\theta below the horizontal, with an initial speed of 30 m s−1^{-1} from a position 90 m above ground level. The object hits the ground 90 m horizontally from its projection point. Use vector calculus to determine θ\theta in its simplest form. Assume that the magnitude of mean acceleration due to gravity on Earth is 10 m s−2^{-2} and that there is no air resistance.
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