SOLUTION: h=H +v(v/g)-(1/2)g(v/g)^2 solve for v

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Question 1203396: h=H +v(v/g)-(1/2)g(v/g)^2
solve for v
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
+h=H+%2Bv%28v%2Fg%29-%281%2F2%29g%28v%2Fg%29%5E2

+h=H+%2Bv%5E2%2Fg-gv%5E2%2F2g%5E2

+h=H+%2Bv%5E2%2Fg-v%5E2%2F2g

+h=H+%2B2v%5E2%2F2g-v%5E2%2F2g

+h-H+=v%5E2%2F%282g%29

+v%5E2=%28h-H+%29%282g%29

+v=sqrt%28%28h-H+%29%282g%29%29

+v=sqrt%282%28gh-gH+%29%29

+v=sqrt%282%29sqrt%28%28gh-gH+%29%29

solutions:

+v+=+sqrt%282%29+sqrt%28g+h+-+g+H%29
or
+v+=+-sqrt%282%29+sqrt%28g+h+-+g+H%29

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
h%22%22=%22%22   

h%22%22=%22%22H+%2Bv%5E2%2Fg%5E%22%22-%281%5E%22%22%2F2%5E%22%22%29g%28v%5E2%2Fg%5E2%29

h%22%22=%22%22

h%22%22=%22%22H+%2Bv%5E2%2Fg%5E%22%22-%281%5E%22%22%2F2%5E%22%22%29%28v%5E2%2Fg%5E%22%22%29

h%22%22=%22%22H+%2Bv%5E2%2Fg%5E%22%22-v%5E2%2F%282g%5E%22%22%29

Multiply through by 2g

2gh%22%22=%22%222gH+%2B2v%5E2-v%5E2

2gh%22%22=%22%222gH+%2Bv%5E2

2gh-2gH%22%22=%22%22v%5E2

2g%28h-H%29%22%22=%22%22v%5E2

%22%22+%2B-+sqrt%282g%28h-H%29%29%29%22%22=%22%22v if h%3E=H

The other tutor left off the fact that the answer is only valid if h%3E=H

If you inadvertently typed a capital H for a little h,
then the answer is 0.

Edwin