qamptr
- 10
- 0
Homework Statement
A projectile is fired from a gun (adjusted to give maximum range) with velocity v_{0}. The projectile passes through two points at a height h. The problem asks us to show that d=\frac{v_{0}}{g}\sqrt{v^{2}_{0}-4gh}
where d is the distance between the two points at height h.
Homework Equations
r=v_{0}t+\frac{1}{2}at^{2}
v=v_{0}+at
x= \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}
The Attempt at a Solution
I was able to get a quadratic function of x:
0=\frac{g}{v^{2}_{0}}x^{2}-x+h
After manipulation using the quadratic formula, all I can see is:
x=\frac{v^{2}_{0}}{2g}+\frac{1}{v_{0}}\sqrt{v^{2}_{0}-4gh}
Which just looks so close but I'm killing myself in trying to see how it is either (1) wrong or (2) able to be simplified.
EDIT: x=\frac{v^{2}_{0}}{2g}+\frac{1}{2gv_{0}}\sqrt{v^{2}_{0}-4gh}, sorry.
Help?
Last edited: