A rectangular block of wood has dimensions 8.0cm×6.0cm×4.0cm and a mass of 0.10kg. The block is coated with a material that experiences a linear resistive force of magnitude kv when moving through water, where v is the speed of the block relative to the water and k=0.040Nsm−1. The block is held completely submerged in calm fresh water and released from rest. Assume the resistive force acts opposite the direction of motion.
(a) Determine the magnitude of the upward force exerted by the water on the block at the instant it is released.
(b) Calculate the initial acceleration of the block just after release.
(c) Derive an algebraic expression for the block’s acceleration a as a function of its instantaneous speed v while it is still completely submerged.
(d) Using your expression from part (c), obtain an expression for the terminal speed vt that the block approaches as it rises.