Problem on parameterization and speed

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An ant is on a merry-go-ground that is rotating clockwise at $\omega$ radians per second. Initially, the ant is at $(R,0)$. From the ant's perspective, it walks toward the center with speed $v$. Several snapshots in time are as follows:
  1. Find the parameterization of the path taken by the ant (relative to the ground)
  2. Compute the speed of the ant as a function of $t$. When is it largest?
  3. Set up, but do not evaluate, an integral for the arc length of the path taken by the ant between $t=0$ and when the ant reaches the origin