18M.2.SL.TZ2.S_6

pestleMathematicsAISLPaper 218M· sl-2-5-modelling-functionssource ↗

At an amusement park, a Ferris wheel with diameter 111 metres rotates at a constant speed. The bottom of the wheel is k metres above the ground. A seat starts at the bottom of the wheel.

The wheel completes one revolution in 16 minutes.

After t minutes, the height of the seat above ground is given by $h\left( t \right) = 61.5 + a\,{\text{cos}}\left( {\frac{\pi }{8}t} \right)$ , for 0 ≤ t ≤ 32.

Find when the seat is 30 m above the ground for the third time.

Markscheme / solution

valid approach (M1)
eg sketch of h and $y = 30,\,\,h = 30,\,\,61.5 - 55.5\,{\text{cos}}\left( {\frac{\pi }{8}t} \right) = 30,\,\,t = 2.46307,\,\,t = 13.5369$

18.4630

t = 18.5 (minutes) A1 N3

[3 marks]

Examiners’ report

[N/A]