- The height above ground, \(H\) metres, of a passenger on a roller coaster can be modelled by the differential equation
$$\frac { \mathrm { d } H } { \mathrm {~d} t } = \frac { H \cos ( 0.25 t ) } { 40 }$$
where \(t\) is the time, in seconds, from the start of the ride.
Given that the passenger is 5 m above the ground at the start of the ride,
- show that \(H = 5 \mathrm { e } ^ { 0.1 \sin ( 0.25 t ) }\)
- State the maximum height of the passenger above the ground.
The passenger reaches the maximum height, for the second time, \(T\) seconds after the start of the ride.
- Find the value of \(T\).