Question

You notice one of the fish has a broken fin, so that it is simply falling in the water under the force of gravity. You measure the terminal velocity of it to be about 0.5 µm/s.it's small, so the drag force from the water is linear proportional to the velocity.
(a)fish have a mass of about 1pg (p=pico). Given this, what is the drag constant b?
(b) What is the time constant,τ = m/b, for the falling fish?
(c) You start your stopwatch when the fish is stopped, right before it starts falling. What is the speed of the fish at t = 0.1τ, t = τ, and t = 3τ? Express your answers as a fraction of terminal velocity, vT (like 0.8vt).
(d) Find the acceleration of the fish at these three times. Express your answer as a fraction of g. This requires you do some calculus on the equation for the velocity as a function of time.