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calculus word problem need help?
If we assume that wind resistance is proportional to velocity, then the downward velocity, v, of a body of
mass m falling vertically is given by v = mg/k(1-e^(-kt/m)
where g is the acceeration due to gravity and k is a constnt. find the height, h, as a function of time. Assume the body starts at t0.
I've gotten as far as integrating it to get h(t). But I don't know if that's all I need to do. It seems there is something I need to do with h0.
i got h(t) = mg/k(t+(me^(-kt/m)/k)) + C
What do I do next?
Or would it just be h0 - mg/k(t+(me^(-kt/m)/k)) + C to find the height given a certain t??
1 Answer
- QLv 61 decade agoFavorite Answer
Initial height and time are known:
h0 = h(t0) = mg/k(t0+(me^(-kt0/m)/k)) + C
Solve for C:
C = h0 - mg/k(t0+(me^(-kt0/m)/k))
Replace C with its value:
h(t) = mg/k(t+(me^(-kt/m)/k)) + h0 - mg/k(t0+(me^(-kt0/m)/k))
