learnmath.bernatchez.net

A Ferris wheel at an amusement park has a diameter of 100 metres. Figure A.

Table of heights of \(P\) in metres above the ground after \(t\) minutes. Table B.

Let \(P\) be a point on the wheel. The wheel starts with \(P\) at its lowest point, at ground level.

The wheel rotates at a constant speed, counter-clockwise. One full rotation takes \(20\) minutes.

1. Find the height of \(P\) above the ground after:
   1. \(10\) minutes.
   2. \(15\) minutes.
2. Let \(h(t)\) be the height of \(P\) above the ground in metres after \(t\) minutes.
   1. Show that \(h(8)=90.5\).
   2. Find \(h(21)\).
3. Sketch the graph of \(h\), for \(0 \leq t \leq 40\).
4. Given that \(h\) can be expressed in the form \(h(t) = a\,\cos\,bt + c\), find \(a\), \(b\) and \(c\).