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 the argument 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.
Show that H=48e−cos(0.2t)H = 48e^{-\cos(0.2t)}H=48e−cos(0.2t).
Find the time, to the nearest minute, that it takes for the ride to reach its maximum height.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.