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?
Parabolas and projectiles
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geometry
algebra-precalculus
physics
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0Thanks,it´s edited. Let´s work with the velocity to eliminate m. How can I work with this variables? – 2012-11-22
1 Answers
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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 $u = \left \vert \dfrac{x}{\cos(c)} \right \vert \sqrt{\dfrac{g}{2(y-x \tan(c))}}$