14. A theme park ride lasts for 70 seconds. The height above ground, \(H\) metres, of a passenger on the theme park ride is modelled by the differential equation $$\frac { \mathrm { d } H } { \mathrm {~d} t } = \frac { t \sin \left( \frac { \pi t } { 5 } \right) } { 10 H } \quad 0 \leqslant t \leqslant 70$$ where \(t\) seconds is the time from the start of the ride.
Given that the passenger is 5 m above ground at the start of the ride find the height above ground of the passenger 52 seconds after the start of the ride.
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