Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 57

A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of \(3.66 \text{ m/s}\) and a centripetal acceleration \(\vec{a}\) of magnitude \(1.83 \text{ m/s}^2\). Position vector \(\vec{r}\) locates him relative to the rotation axis. (a) What is the magnitude of \(\vec{r}\)? What is the direction of \(\vec{r}\) when \(\vec{a}\) is directed (b) due east and (c) due south?