Physics
posted by Mary .
A large solid cylinder rolls without slipping down a 40 m long hill with a 30 degree slope. The cylinder then rolls a short distance over level ground and then off a 20 meter high sheer cliff. How far from the base of the cliff does the cylinder land? Ignore friction and air resistance

The law of conservation of energy
PE =KE,
PE = m•g•h = m•g•s•sinα,
KE = KE1 + KE2 = m•v^2/2 + I•ω^2/2=
= m•v^2/2+ (m•R^2/2) •v^2/2•R^2 =
=3•m•v^2/4.
m•g•s•sinα =3•m•v^2/4.
v = sqrt(4• m•g•s•sinα/3) = 16.2 m/s.
H =gt^2/2, t = sqrt(2•H/g) = 2.02 s.
L =v•t = 16.2 • 2.92 = 32.7 m. 
Thank you so much, Elena!