Answer
The radius of the circle is 18.6 meters.
Work Step by Step
We can find Jack's speed $v$.
$v = (0.100~rev/s)(\frac{2\pi ~r~m}{1~rev})$
$v = (0.2\pi ~r)~m/s$
We can find the radius of the circle.
$\sum F = \frac{mv^2}{r}$
$mg - F_N = \frac{m~(0.2\pi ~r)^2}{r}$
$mg - 0.25~mg = {m~(0.2\pi)^2~r}$
$0.75~g = {(0.2\pi)^2~r}$
$r = \frac{0.75~g}{(0.2\pi)^2}$
$r = 18.6~m$
The radius of the circle is 18.6 meters.
