Standard +0.3 This is a straightforward separable variables question requiring separation to H dH = (t sin(πt/5)/10) dt, integration of both sides (the RHS requires integration by parts but is routine), and substitution of initial condition H(0)=5 and evaluation at t=52. While it involves multiple steps and integration by parts, it follows a completely standard template with no conceptual challenges or novel insights required.
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. [0pt]
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.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q14 [6]}}