A boy is spinning a rock around in a horizontal circle over his head. The rock is tied to a string. The child is unsuccessfully trying to kill pigeons with his rock by letting it go and watching it fly towards the dirty$-$rat$-$with$-$wing birds. Anyhow, the rock is currently spinning with a more or less constant speed of $3\mathrm{.}5$ m$/$s$.$ During a half rotation, the rock changes its velocity from North to South, over the course of $0\mathrm{.}46$ s$.$ Draw an overhead view diagram of the situation, and determine:

a$)$ The acceleration of the rock during this half rotation

b$)$ The radius of the circle that the rock is travelling in $($this is the length of the rope that the boy is holding!$)$