I have two projectiles that are launched at different times. The one that is launched second should collide with the first one mid-air. Given are the launch angles αP1&αP2, start speeds v0P1&v0P2 and start positions(x0P1/y0P1)&(x0P2/y0P2) of both projectiles. I'm looking for the launch time of the second projectile so that $$ y0_P1+(v0_P1⋅sin(α_P1))⋅t1−(1/2)⋅g⋅t1^2=y0_P2+(v0_P2⋅sin(α_P2))⋅t2−(1/2)⋅g⋅t2^2 $$ $$x0_P1+(v0_P1⋅cos(α_P1))⋅t1=x0_P2+(v0_P2⋅cos(α_P2))⋅t2$$
As projectile is launched after the first, t2=(t1+tOffset). Now I tried to solve the above equations for tOffset and but didn't really get anywhere. Is this the correcty way to get what I'm looking for?
Thanks in advance
I suggest eliminating $t$ from the two sets of equations to get an equation of the form $$y=y_0+(x-x_0)\tan\alpha+{g\over2v_0^2\cos^2\alpha}(x-x_0)^2$$ for each parabola. Subtracting one from the other will give you a quadratic equation in $x$ for the intersections of the two parabolas. Assuming that there are any intersections, it’s a simple matter to compute the travel times of the two projectiles to those $x$-coordinates and then find their difference. You’ll need to discard any solution for which either of the times or the difference between the second and first is negative, of course.