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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 $(t,\theta)$: $$x_{0t}+v_{xt}t=x_{0a}+v_{a}\cos\theta t \\ y_{0t}+v_{yt}t=y_{0a}+v_{a}\sin \theta t$$

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Hi, thanks for the response. I'm a programmer by trade and this isn't something Ive covered at school before. I am relatively good at maths, but would you mind explaining this a bit? At the moment I'm assuming t is the time and [insert theta here] is the angle between the two lines from the arrow to the object's initial position and the line such that they collide. Thanks! – user3240643 Feb 27 '14 at 18:47
Just to clarify, what I don't understand is: The format of the positions (I only know the Cartesian system, - (x,y)); and the symbols. – user3240643 Mar 1 '14 at 11:24

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