Answer
$K = 7.6\times 10^8~J$
Work Step by Step
We can find an expression for the speed:
$v = \frac{distance}{time} = \frac{2\pi~r}{T}$
In part (a), we found that the radius of the orbit is $~~1.9\times 10^7~m$
We can find the kinetic energy:
$K = \frac{1}{2}mv^2$
$K = \frac{1}{2}m(\frac{2\pi~r}{T})^2$
$K = \frac{2\pi^2~m~r^2}{T^2}$
$K = \frac{(2\pi^2)~(50~kg)~(1.9\times 10^7~m)^2}{(21,600~s)^2}$
$K = 7.6\times 10^8~J$
