Parametric, Polar and Vector-Valued Functions · Superchallenge problem

A wheel of radius $1$ rolls along the $x$-axis, and a point on its rim traces the cycloid $x=t-\sin t$, $y=1-\cos t$, starting on the ground at $t=0$. At the moment when the point has travelled a total distance of $1$ along its path, how high above the ground is it?