Horizontal disk of mass M is constrained horizontally, but is free to move verti

Question

Horizontal disk of mass M is constrained horizontally, but is free to move vertically. A jet of fluid strikes the disk from below. The jet leaves the nozzle at initial speed Vo. The fluid jet decelerates to velocity V1 before it hits the plate due to gravity on the jet. The plate sits at an equilibrium height of ho above the jet exit plane. At the equilibrium position the net force on the plate is 0. -> Apply the integral momentum equation to find an equation for the equilibrium height ho? Picture below should be vertical.

Explanation / Answer

Mass=M

initial speed Vo

So.

Using momentum and energy conservation :
momentum before collision :

mVo , momentum after collision :

mV1 + MV2
mVo = MV2 + mV1

and at equilibrium : conserving energy :

0.5mVo^2 = 0.5mv1^2 + Mgdho
hence

ho = (1/Mdg)*(0.5mVo^2 - 0.5mv1^2)

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