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3.6 Integration (A-level only)

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Question 26

The height of a passenger on a Ferris wheel above the ground, H H\,H metres, is modelled by the differential equation

dHdt=Hsin⁡(0.2t)5\displaystyle \frac{dH}{dt} = \frac{H\sin(0.2t)}{5}dtdH​=5Hsin(0.2t)​

where t t\,t is the time in minutes from the start of the ride and t t\,t is measured in radians.

The passenger is 48e\dfrac{48}{e}e48​ metres above the ground at the start of the ride.

a.

Show that H=48e−cos⁡(0.2t)H = 48e^{-\cos(0.2t)}H=48e−cos(0.2t).

[5]
b.

Find the time, to the nearest minute, that it takes for the ride to reach its maximum height.

[2]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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