It is a beautiful afternoon, and Jose is considering taking a leisurely two-hour stroll through the park. There are several other activities Jose is considering doing instead. The value Jose receives from each of the activities is provided in the table.

(a) The water level in the pool when the cube is on the bottom of the pool is the same as when the cube is on the raft

(b) The force exerted by the crane on the cube is the same in both cases

Explanation:

a. Here we note that Archimedes's principle states that for a body immersed, either wholly or partial in a fluid, the buoyancy or upward force acting on the body in the fluid is equal to the wight of the displaced fluid. Since the raft and the cube form a system experiencing an upward force equal to their weight, then, for the raft to float, the volume displaced is equal to the weight of the raft plus the metal cube. When the cube sinks the fluid, there is less weight on the raft, so it rises while the water level remain  the same as the proportionate amount of volume is taken up by the cube and the floating raft.

b. Where the bottom of the cube is at a depth of 2.0 m we have a buoyant force acting from the bottom of the cube and weight of  the fluid over head acting from the top

Buoyant force - Weight of cube - weight of 2.0 m column of water above + Upward force due to pressure acting from beneath the cube at (2+0.45 m)

When the cube is at 4.0 m we have the buoyant we have

Buoyant force - Weight of cube - weight of 4.0 m column of water above + Upward force due to pressure acting from beneath the cube at (4+0.45 m)

Therefore the force exerted by the crane on the cube is constant in both cases.