Answer
a) 3.6 meters
b) 4.8 seconds
Work Step by Step
a)
Using law of conservation of energy equation:
$0.5mv_{i}^{2}+0.5Iw^{2}=mgh$
Since the masses cancel out:
0.5(9) +0.5(9) = 9.8(h)
The vertical height is then found to be 0.92, however we want the hypotenuse length, so given the angle of 15 we can determine that:
d=0.92sin15
d = 3.6 meters
b)
Given the hoop will be going up the ramp and down without friction we can assume the total distance on the ramp will be 2*3.6. Then;
$d=0.5(v_{i}+v_{f})t$
7.2 = 0.5(3 + 0)t
t = 4.8 Seconds
