The maximum height that a roller coaster can reach is $90$ meters above sea level, and the lowest

Question

The maximum height that a roller coaster can reach is $90$ meters above sea level, and the lowest possible height is $10$ meters above sea level. The roller coaster takes $10$ seconds to move from its highest position to its lowest position. The height, $h$ m, of the roller coaster above sea level can be modelled by the function $h = a \cos \left( \frac{\pi}{b} t \right) + c, \text{ where}\hspace{0.5em} t \text{ is the time in seconds.}$ Show that $h = 40 \cos \left( \frac{\pi}{10} t \right) + 50$.[3] Sketch the graph of $h = 40 \cos \left( \frac{\pi}{10} t \right) + 50$ for $0 \le t \le 30$.[2] Find the time when the roller coaster first reaches a height of 62 m.[2] On your graph in part (b), draw a graph of $h=t+15$ State for the interval $0 \leq t\leq 30$, the number of solutions of $t=40\cos(\frac{\pi}{10}t)+35$.

Accepted Answer

(c)t=4.03s (d)(ii)3

2025 MGS PRELIMS P1 Q10

2025 MGS PRELIMS P1 Q10