The height of a Ferris wheel above the ground, H H\,H metres is modelled by the differential equation:
dHdt=Hsin(0.2t)5 \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.
Given that the passenger is 48e\displaystyle \frac{48}{e}e48 m 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, it takes for the ride to reach its maximum height.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.