Answer
$K = 61.7~J$
Work Step by Step
The rotational inertia of a solid sphere is $I = \frac{2}{5}MR^2$
We can find the total kinetic energy:
$K = \frac{1}{2}Mv^2+\frac{1}{2}I\omega^2$
$K = \frac{1}{2}Mv^2+\frac{1}{2}(\frac{2}{5}MR^2)(\frac{v}{R})^2$
$K = \frac{1}{2}Mv^2+\frac{1}{5}Mv^2$
$K = \frac{7}{10}Mv^2$
$K = \frac{7}{10}(\frac{36.0~N}{9.8~m/s^2})(4.90~m/s)^2$
$K = 61.7~J$
