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Rates of change and differential equations — Question 17

QCAA 2023, Paper 2 · 6 marks

Q17 · 2023 · Technology-activeComplex familiar6 marks

QUESTION 17 (6 marks)

An object is projected upwards from ground level with an initial velocity of 15 m s−1^{-1} at an angle of 54∘54^\circ to the horizontal. The object just passes over a drone hovering in the air. An observer is positioned directly below the drone and at a horizontal distance of 20 m from where the object is projected. The observer commented that: • it took the object around 2 to 2.5 seconds after its projection to reach the drone • the object was still moving in an upwards direction as it passed the drone. Assuming that air resistance is negligible, use a vector calculus approach to evaluate the reasonableness of the observer’s comments.
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