If two objects travel through space along two different curves, it\'s often impo
ID: 2856705 • Letter: I
Question
If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time.
Suppose the trajectories of two particles are given by the vector functions. r1(t) = r2(t) = <17t 72, t2, 11t 24> for t 0.
Find the values of t at which the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
Explanation / Answer
Given the vector position for both particles:
r1(t) = r2(t) = <17t -72, t2, 11t - 24>,
In this case, we just need to analyze that both particles has the same vector position, and at any time one particle will be following the other one. (Also we can focus on the information provided; first paragraph).
On this way, we can say that the particles DO NOT collide.
So the answer is DNE.
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