I have been struggling with this problem for a while:
A bullet passes through a piece of wood 0.1 m thick. It enters the wood at 400 m/s and leaves at 180 m/s. The velocity v of the bullet is assumed to obey the differential equation dv/dt = -kv^2 where k is a positive constant. How long does it take the bullet to pass through the wood?
I got this far:
dv/dt = -kv^2
-1/v = -kt + C
v = 1/(kt + C)
400 = v(0) = 1/(k(0) + C)
400 = 1/C
.0025 = C
v = 1/(kt + .0025)
From here, I am not sure what to do. I tried to find k by making v = dx/dt and solving the displacement equation, which turned out to be another dead end.
Any help would be appreciated. Thanks.