I don\'t understand where 6/5 came from, but the rest is similar to our books ex

Question

I don't understand where 6/5 came from, but the rest is similar to our books example. The teacher's example follows F=mgsin theta - f=ma and then substitutes f=2ma/3 for friction in that equation. The book example makes more sense to me, but I'm not coming up with the correct answer which is time=1.7s and acceleration of 2.94 m/s^2.

A regulation basketball has a 25 cm diameter and may be approximated as a thin spherical shell. The acceleration of gravity is 9:81 m/s2. How long will it take a basketball starting from rest to roll without slipping 4 m down an incline that makes an angle of 30 degrees with the horizontal? Answer in units of s. The given moment of inertia is I = 2/3 MR^2


Energy considerations: ½mv² + ½I?² = mgh
I = (2/3)mr², ? = v/r and h = 4sinT ?
v = v((6/5)*g*4sin30°) = m/s

t = 2x/v = 2*4/velocity = t sec

Explanation / Answer

I = 2/5 m r^2 ------(1)
and v = r -----(2)

so, ½mv² + ½I² = mgh

½mv² + ½(2/5m)(r)² = mgh

using (1) and (2)

½mv² + 1/5(m)(v)² = mgh

7/5 m v² = mgh

v = 5*gh/7

I'm sure this is the proper soultion to ur problem, that 6 should not be there. ur teacher also must have made a mistake

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