- #1
Burjam
- 52
- 1
Homework Statement
Suppose water leaks out of a barrel at a rate proportional to the square root of the depth of the water. If the level starts at 36 in. and drops to 35 in. after 1 hour, how long will it take for all the water to leak out of the barrel?
I have to choose and implement a differential equation solution method to determine a solution.
Homework Equations
N/A
The Attempt at a Solution
dL/dt = -√(L), where L is the water level and t is time in hours
∫dL/-√(L) = ∫1dt
-2√(L) = t + c
L = ((t+c)/2)^2
36 = (-c/2)^2
c = 12
So now that I've solved for the constant using the initial condition, I'm not sure what to do. I think I might've even set up this problem wrong to begin with because when I substitute 1 in for t, I don't get 35, which is what L should equal at that t.
Help.