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If we throw a ball from the hight point $h$ from the earth, with initial velocity $v’$, how to prove that the time it takes the ball to reach the earth is given by:

$$t=\frac{v}{g}(1+\sqrt{1+\frac{2hg}{v^2} } )$$

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You work with the equations of motion. BTW, is this a homework type problem? –  ja72 Sep 26 '12 at 13:32
    
Why the question was tagged as a homework ? It's not –  rib Sep 26 '12 at 14:56
    
Did you check the homework tag description? –  Qmechanic Sep 26 '12 at 15:38
    
@Qmechanic Sorry no,but i know that you shouldn't tag the question as a homework unless if the OP say that blatantly. –  rib Sep 26 '12 at 15:47
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@rib This won't work -- hard core do-my-job OPs will never admit their question is a homework problem. –  mbq Oct 7 '12 at 11:35
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1 Answer

For a free falling object without air resistance you have two equations

$$ y = h + v'\,t - \frac{1}{2} g t^2 $$ $$ v = v' - g\,t $$

with $h$ the initial height, $v'$ the initial velocity (upwards is positive), $y$ the height at time $t$, and $v$ the velocity.

Solve them when $y=0$ for $v$ and $t$.

Reference: projectile motion.

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equations should be $ v_{f}=V_{0}+gt $ and $ h=v_{0} t+1/gt^{2} $ the equation for the high is a second order equation yu can solve it immediatly for 't' –  Jose Javier Garcia Sep 26 '12 at 15:02
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