Posted by Soroban on September 09, 2002 at 13:16:12:
In Reply to: Sorry... solution equation is wrong! posted by colin on September 09, 2002 at 11:19:14:
: : Here's the problem:
: I mistyped the solution equation for the problem. The correct equation for the solution (from the book) is:
: 2m/k(sqrt[v0]-sqrt[v]) + 2m^2g/k^2* ln[(mg-kSqrt[v0])/(mg-kSqrt[v])] = t
They DID make two integrals out of it.
Look at that integral: INT dv/[g - c*Sqrt(v)]
It will take a substitution: u = Sqrt(v).
Then v = u^2, and dv = 2u du
The integral becomes: INT 2u du/(g - cu),
which will require some long division (or some
trick like "adding zero").
And THAT's why there are two integrals.
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