# Finding the point at which two objects will collide (analogous to aiming an arrow at a moving target)

Assuming I have a moving target, whose location, speed and direction I know, and a arrow, whose location and speed I know, is it possible to find the point at which the two will hit?

A real-world analogy is aiming an arrow at a moving target. How do we know where to shoot? Is it possible to actually find the point at which they will collide?

Thank you,

PS: I don't mind whether you work out the point's coordinates, the distance from the object whose direction is known, or anything which helps me define whereabouts it is.

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Let your target be at position $(x_{0t}+v_{xt}t,y_{0t}+v_{yt}t)$ and the arrow be $(x_{0a}+v_{xa}t,y_{0a}+v_{ya}t)=(x_{0a}+v_{a}\cos\theta t,y_{0a}+v_{a}\sin \theta t)$ To meet, they need to be at the same place, giving two equations in two unknowns $(t,\theta)$: $$x_{0t}+v_{xt}t=x_{0a}+v_{a}\cos\theta t \\ y_{0t}+v_{yt}t=y_{0a}+v_{a}\sin \theta t$$