\[(0,67.5)\]
.A point on the wheel rotates at the rate
\[2 \pi\]
per 30 minutes, or \[\frac{2 \pi}{30 \times 60}= \frac{\pi}{900} rads/sec\]
. In a times \[t\]
the wheel will rotate through an angle \[\theta = \frac{\pi}{900}t\]
. The London eye appears to rotate in the clockwise as seen from the other side of the Thames. By convention, clockwise is negatives, so the angle of rotation is \[- \frac{\pi}{900}t\]
.By convention also the horizontal line is taken as the zero angle, so at any times
\[t\]
, the position of a point that started from the ground at \[t=0\]
is \[(67.5sin(- \frac{\pi}{900}t), 67.5-67.5cos(- \frac{\pi}{900}t)\]
.