If two objects travel through space along two different curves, it is often impo
ID: 3193949 • Letter: I
Question
If two objects travel through space along two different curves, it is often important to know whether they will collide. The curves might intersect showing that objects will be in the same location at some time, but we need to know whether the objects are in the same location at the same time . Suppose the trajectories of two objects are given by r1(t)= and r2(s)=<1+3s, 1 +9s,1+36s> Find two points where the trajectories intersect. Enter the point with the smaller x -value first. point=( , , ) at t = and s= point=( , , ) at t = and s= Do the objects ever collide?Explanation / Answer
If you have the trajectory defined by certain formulas (for x and y or whatever) then I think I would try fixpoint iteration. Else it will be somewhat more complicated. If you have pure data I would try to interpolate the points as I approach the fixpoint. You define the amount of iterations in order to recieve a sufficently good approximatoin of the solution and in each step you interpolate the vectors in a more and more narrower interval of the vectors defining the trajectory. I think this is how I would approach the problem of yours.