Answer
1.163 meters
Work Step by Step
We use conservation of energy to obtain:
$mgh = \frac{1}{2}mv^2+\frac{1}{2}\frac{2}{3}mr^2\omega^2 \\mgh = \frac{1}{2}mv^2+\frac{2}{6}mr^2\omega^2 \\mgh = \frac{1}{2}mv^2+\frac{2}{6}mr^2\frac{v^2}{r^2} \\ 2gh = \frac{1}{2}v^2+\frac{2}{6}v^2\\ h = \frac{\frac{5}{6}v^2}{g}= \frac{\frac{5}{6}(3.7)^2}{9.81}=\fbox{1.163 meters}$
