9. A 2mx2mx1m block is held with its bottom just touching the water surface (see figure...

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9. A 2mx2mx1m block is held with its bottom just touching the water surface (see figure below), then released from rest at t=0. Assume that the block moves only vertically with its bottom remaining parallel to the water surface, and the water density is 1000 kg/m. The block has a mass of 2000 kg and dh its motion is resisted by a force with magnitude a where a is 4000 kg/s. dt Initial position of block, at rest with bottom just touching water surface. 2 m block top 2 m 2 m air block side 1 m th water (a) Derive a differential equation that governs the vertical motion of the block for t0. Include the initial conditions. (b) Solve for the block depth as a function of time h(t). (c) What is the steady-state depth of the block? 9. A 2mx2mx1m block is held with its bottom just touching the water surface (see figure below), then released from rest at t=0. Assume that the block moves only vertically with its bottom remaining parallel to the water surface, and the water density is 1000 kg/m. The block has a mass of 2000 kg and dh its motion is resisted by a force with magnitude a where a is 4000 kg/s. dt Initial position of block, at rest with bottom just touching water surface. 2 m block top 2 m 2 m air block side 1 m th water (a) Derive a differential equation that governs the vertical motion of the block for t0. Include the initial conditions. (b) Solve for the block depth as a function of time h(t). (c) What is the steady-state depth of the block?