(1) From an energy point of view the kinetic energy of the block has to balance the potential energy due to gravity. As the block is pushed along the slope, its potential energy increases. When KE=PE the block reaches its highest position x from the ground. So max=½mv², or 2gx=v² and x=v²/(2g)=25/19.62=1.274m. But this is the vertical height. The distance along the slope is H and x=Hsinθ so H=x/sinθ=v²/(2gsinθ)=25/(19.62×sin53)=1.60m approx.
(2) The hoop has translational and rotational kinetic energy: ½mv²+½I⍵² where I=mr² for a hoop and ⍵=v/r, so the rotational KE=½(mr²)(v²/r²)=½mv². Therefore we have total KE=mv²=mgx, so x=v²/g and h=v²/(gsinθ)=3.19m.
(3) So h/H=2.