(a) Determine a differential equation for the velocity v(t) of a mass m sinking in water that imparts a resistance proportional to the square of the instantaneous velocity (with is given by Archimedes' principle, which states that the upward buoyant force has magnitude equal to the weight of the water displaced. Assume that the positive direction is
acceleration due to gravity.)
dv ku2
PV
dt
g-
m
m
(b) Solve the differential equation in part (a).
v(t) =
mg-PV
.2
k
mg -pykt
k
- +
m
X
(c) Determine the limiting, or terminal, velocity of the sinking mass.
lim v(t) =
mg - PV
k
t-
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