## Position of Point on London Eye Relative to Ground

\[(0,67.5)\]

.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 \[(67.5sin(- \frac{\pi}{900}t), 67.5-67.5cos(- \frac{\pi}{900}t)\]

.