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.
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.
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.