Given $2$ points, $A$ and $B$, if I am in $A$ and I have an inclination angle $c$, with how many velocity do I need to shoot a projectile to hit $B$ ? My problem is, how do I setup this data in an equation so that I can solve it with a program?
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$\begingroup$ Strength is an elusive concept. Do you actually mean velocity? Then it would be independent of mass. If you mean force, one would need to know how long the force was applied. $\endgroup$– André NicolasNov 22, 2012 at 2:21
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$\begingroup$ Thanks,it´s edited. Let´s work with the velocity to eliminate m. How can I work with this variables? $\endgroup$– chubakuenoNov 22, 2012 at 2:27
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1 Answer
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Let $A$ be the origin and $B$ be $(x,y)$. The angle of projecting is $c$. The parabolic trajectory is given by the formula below
$$y = x \tan(c) - \dfrac{g}{2u^2 \cos^2(c)}x^2$$
This gives us $$u^2 = \dfrac{gx^2}{2 \cos^2(c) (y-x \tan(c))}$$
Hence the unique velocity is $$u = \left \vert \dfrac{x}{\cos(c)} \right \vert \sqrt{\dfrac{g}{2(y-x \tan(c))}}$$