If a projectile is launched from the floor, and lands at an elevated height how would one find the initial velocity given only (angle of launch, angle of ending elevation, total distance, and gravity?
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1 Answer
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For projectiles, the equations of motion can be separated into the horizontal and vertical motions: $$x(t) = V_x*t$$ $$y(t) = V_y*t-\frac 12*g*t^2$$
If this figure is reasonable for the problem, then there are two equations and two unknowns (the initial velocity V and time of impact $t_i$). You just need to solve these two equations for V and $t_i$ since everything else is given in the problem statement.
$$x(t_i) = d*\cos(\theta) = V\cos(\alpha)*t_i$$ $$y(t_i) = d*\sin(\theta) = V\sin(\alpha)*t_i - \frac 12*g*t_i^2$$
