Answer:
(A) h = 4.9 m v
(B) = 8 m/s
Explanation:
translational speed = 7.6 m/s
(A) from the conservation of energy equation
mgh = (mv^{2} / r) + (Iw^{2} / r)
where the moment of inertial (I) = (2mr^{3}) / 3
mgh = \frac{mv^{2}}{r} + \frac{\frac{2mr^{3}}{3} x w^{2} }{r}
mgh = m (\frac{v^{2}}{r} + \frac{\frac{2r^{3}}{3} x w^{2} }{r} )
gh = \frac{5V^{2}}{6}
g = \frac{5V^{2}}{6g}
h = \frac{(5) x (7.6)^{2}}{6 x 9.8}
h = 4.9 m
(B) just as from in (A) above, using the conservation of energy equation with (I) being close to mr^2 / 2
mgh = (mv^{2} / r) + (1/2)(mr^{2}/2)(v/r)^{2}
v = [tex]\sqrt{\frac{4gh}{3} }[/tex]
v = [tex]\sqrt{\frac{4 x 9.8 x 4.9}{3} }[/tex]
v = 8 m/s
