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Rates of change and differential equations — Question 19

QCAA 2022, Paper 2 · 7 marks

Q19 · 2022 · Technology-activeComplex unfamiliar7 marks

QUESTION 19 (7 marks)

A research organisation plans to use a drone to drop a scientific instrument vertically from a stationary position above the ocean surface. The acceleration (m s−2^{-2}) of the falling instrument can be modelled by 9.8−0.1v9.8-0.1v, where vv is its velocity (m s−1^{-1}). In order for the instrument sensors to activate, its speed as it hits the ocean surface must reach at least 20 m s−1^{-1}. However, if it hits with a speed above 50 m s−1^{-1}, the sensors will be damaged. Determine the range of the drone’s flying height above the ocean surface to ensure that the sensors are activated but not damaged.
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