Answer
The box has fallen a distance of $~~0.27~m$
Work Step by Step
In part (a), we found that the wheel's rotational kinetic energy is $~~10~J$
We can use conservation of energy to find the distance the box has fallen:
$mgh = 10~J+6.0~J$
$h = \frac{16~J}{mg}$
$h = \frac{16~J}{(6.0~kg)(9.8~m/s^2)}$
$h = 0.27~m$
The box has fallen a distance of $~~0.27~m$
