Mathematics

Problem

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\in\mathbb{R}

. Find the values of

a

b

and

c

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