Date | May 2021 | Marks available | 5 | Reference code | 21M.2.SL.TZ1.4 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 1 |
Command term | Find | Question number | 4 | Adapted from | N/A |
Question
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(bt)+c, where a, b, c ∈ ℝ.
Find the values of a, b and c.
Markscheme
amplitude is 1102=55 (A1)
a=-55 A1
c=65 A1
2πb=20 OR -55 cos(20b)+65=10 (M1)
b=π10(=0.314) A1
[5 marks]