math - 2D spcae: How to do vector prediction for intersect point of one circular motion & one linear motion object? -

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in 2d space,

object in uniform circular motion around fixed point..

object b in linear motion, trying target & hit object a..

(eg: bullet (object b) trying hit pole on marry-go-round (object a) in top-down prespective)

assuming both of speeds constant, how can calculate intersection point, i.e. target object b? know direction of object b has take from initial position collide object a..

i have looked around solutions vector predictions 2 linearly moving objects.. appericate tips or advices!!

when object (in case a) moving along circular path, it's position on time t can described as:

x1 = r x cos (w . t) y1 = r x cos (w . t)  w uniform angular speed in radians/second

on other hand, linear speed 

x2 = velocity x time x cos (theta) y2 = velocity x time x sin (theta)

now collision/hitting means:

x1 = x2 y1 = y2

just solve above linear equations t , theta. direction starting point of bullet , point (x, y).


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