Hello,
There are several equations need to be solve together.
v'[t] == k*s*Sqrt[2*9.8*h]
r == Sqrt[1 - (1 - h)^2]
v'[h] == -Pi*r^2
k == 0.62
s == 10^-4
- When t equals 0,
h(t)==1
So, I make out code as
DSolve[{D[v[t, h], t] == k*s*Sqrt[2*9.8*h], r == Sqrt[1 - (1 - h)^2],
D[v[t, h], h] == -Pi*r^2, k == 0.62, s == 10^-4, h[0] == 1}, v, {t,
h}]
I know this is not correct, at least h[0]==1
is not correct. How to find the relationship between t and h?
This one can work but not give correct answer
DSolve[{D[v[t, h], t] == k*s*Sqrt[2*9.8*h],
D[v[t, h], h] == -Pi*r^2}, v, {t, h},
Assumptions -> {r == Sqrt[1 - (1 - h)^2], k == 0.62, s == 10^-4,
h == 1 /; t == 0}]
The answer should be t == 1.068*10^4*(1 - 10/7*h^(3/2) + 3/7*h (5/2))
Thanks.