i got 43 as my first answer and it wasnt right. neither was this one... Problem

Question

i got 43 as my first answer and it wasnt right. neither was this one...

Problem 12.35 Part A A solid sphere of radius R is placed at a height of 38 cm on a 15° slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius R be released on the same slope in order to equal the sphere's speed at the bottom? Express your answer to two significant figures and include the appropriate units. HA 40 h Submit Mv Answers Give Up Incorrect; Try Again; 3 attempts remaining Continue

Explanation / Answer

for sphere, m g h = 1/2 I w2 + 1/2 m v2

m g h = 1/2 (2/5 m R2) (v / r)2 + 1/2 m v2

m g h = 7/10 m v2

v = sqrt [10/7 * g * h]

for hoop, m g h = 1/2 I w2 + 1/2 m v2

m g h = 1/2 ( m R2) (v / r)2 + 1/2 m v2

m g h = m v2

h = v2 / g = [10/7 * g * H] / g = 10/7 * H

h = 10/7 * 38 cm

h = 0.542 m = 54.2 cm

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