An object of density pa, volume Va, and weight Wa is thrown from a rowboat floating on the surface of a small pond and sinks to the bottom. The weight of the rowboat without the jettisoned object is Wb. Before the object was thrown out, the depth of the pond was hp1, and the bottom of the boat was a distance hb1 above the pond bottom. After the object sinks, the values of these quantities are hp2 and hb2. The area of the pond is Ap; that of the boat is Ab. Ab may be assumed constant, so that the volume of water displaced by the boat is Ab (hp – hb).
(a) Derive an expression for the change in the pond depth (hp2 – hp1). Does the liquid level of the pond rise or fall, or is it indeterminate?
(b) Derive an expression for the change in the height of the bottom of the boat above the bottom of the pond (hb2 – hb1). Does the boat rise or fall relative to the pond bottom, or is it indeterminate?