Initially w=v/r
Ei=mv2
finally... w doesnot changes.. but v becomes v/2 (in forward direction and momentum conservation...)
v in upward direction=0(max ht)
so mv2=mgh+1/2m(v/2)2+1/2m(v/2)2+1/2mr2w2
mv2=mgh+1/2m(v/2)2+1/2m(v/2)2+1/2mv2 .w=v/r
so h=v2/4g