21M.2.SL.TZ1.4

pestleMathematicsAASLPaper 221M· sl-3-7-circular-functions-graphs-composites-transformationssource ↗

A Ferris wheel with diameter $110$ metres rotates at a constant speed. The lowest point on the wheel is $10$ metres above the ground, as shown on the following diagram. $P$ is a point on the wheel. The wheel starts moving with $P$ at the lowest point and completes one revolution in $20$ minutes.

The height, $h$ metres, of $P$ above the ground after $t$ minutes is given by $h (t) = a \cos (b t) + c$ , where $a, b, c \in ℝ$ .

Find the values of $a$ , $b$ and $c$ .

Markscheme / solution

amplitude is $\frac{110}{2} = 55$ (A1)

$a = - 55$ A1

$c = 65$ A1

$\frac{2 π}{b} = 20$ OR $- 55 \cos (20 b) + 65 = 10$ (M1)

$b = \frac{π}{10} (= 0.314)$ A1

[5 marks]

Examiners’ report

[N/A]