Answer
a) $v=3.3\frac{m}{s}$
b) $v=2.8\frac{m}{s}$
Work Step by Step
(a) We know that
$mgh=\frac{1}{2}mv^2+\frac{1}{2}(\frac{1}{2}mr^2)(\frac{v}{r})^2$
$\implies gh=\frac{1}{2}v^2+\frac{1}{4}v^2=\frac{3}{4}v^2$
This can be rearranged as:
$v=\sqrt{\frac{4}{3}gh}$
We plug in the known values to obtain:
$v=\sqrt{\frac{4}{3}(9.8)(0.82)}$
$v=3.3\frac{m}{s}$
(b) We know that
'$gh=\frac{1}{2}mv^2+\frac{1}{2}(mr^2)(\frac{v}{r})^2$
$gh=\frac{1}{2}v^2+\frac{1}{2}v^2=v^2$
$\implies v=\sqrt{gh}$
We plug in the known values to obtain:
$v=\sqrt{9.81(0.82)}$
$v=2.8\frac{m}{s}$
