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1.11 H: Integration

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Question 40

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. The angle 0.2t 0.2t\,0.2t 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

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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