Question

Suppose you wish to dispose of nuclear waste by placing it in sealed drums and dropping
the drums into the ocean. Each lled drum weighs 1280 lb and has a volume of 18 cubic
feet. The force equation for a drum falling though water is:
m dv/dt = -W + B + FR
where W is the weight of the drum, B is the buoyant force equal to the weight of
the water displaced by the drum (the density of water is 62.5 pounds per cubic foot),
and FR is the force of water resistance, known to be 1 lb for every ft/s that the drum is
moving. The drums may burst if they hit the ocean
oor at a speed higher than 120 ft/s.
Note: A technology check is expected for computations. Any claimed numeric an-
swer, symbolic answer or equation should be veri ed. If a technology answer check is
impossible, then provide on paper whatever details are possible.
(a) Find an expression for the velocity v(t).
(b) Find the time t at which the drum velocity absolute magnitude is 120 ft/s.
(c) If no initial velocity is given to the drums, what is the deepest water into which the
drums can be dropped without violating the bursting rate 120 ft/s?

Answer 1