Posted by Nikki on Thursday, November 10, 2011 at 12:38am.
Use conservation of energy and include the rotational kinetic energy, (1/2) I w^2. They should have told you whether the sphere has uniform density or is hollow inside. It makes a difference.
For a uniform-density sphere,
M g H = (1/2) M V^2 + (1/2) I w^2
= (1/2) M V^2 + (1/2)(2/5)M R^2*(V/R)^2
= (7/10)M V^2
M cancels out. H is the elevation loss, 6.0 sin 31 = 3.09 meters
Solve for V, the final velocity. For the final angular speed, use
w = V/R
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