Angular Momentum & Moment Of Inertia

1. The problem statement, all variables and given/known data

Two children on opposite ends of a merry-go-round of radius 1.6 m throw baseballs at the same speed of 30 m/s but in opposite directions as shown. The mass of each baseball is 0.14 kg, and the moment of inertia of the merry-go-round and children combined is 180 kg-m^2. If the merry-go-round is initially at rest, what is the linear speed at which the children are moving after the balls have been thrown?

2. Relevant equations

L = Iω
KE = 1/2 Iω^2
KE = 1/2 mv^2
τ = Iα

3. The attempt at a solution

Since the motion of the merry-go-round, on my assumption, is caused by the torque generated by the two baseballs being thrown, the Kinetic Energy caused by the two balls is equal to the Kinetic Energy of the merry-go-round after the throw. Hence, assuming KE is conserved:

2(1/2mv^2) = 1/2 Iω^2
0.14 x 30 x 30 = 0.5 x 180 x ω^2
ω = 0.837
therefore V= ωr
so V = 1.339 m/s

which turns out to be wrong, the correct answer should be 11.9 cm/s or 0.119 m/s.
Is it something wrong with the formulas I’m using or is it just a mistake in my assumptions.
Thank you for your help

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