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If two objects travel through space along two different curves, it is often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) Their paths 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 following vector functions. r₁(t) = (t², 13t 42, t²), r₂(t) = (11t - 30, t², 10t - 24) for t 20 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.)

If two objects travel through space along two different curves, it is often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) Their paths 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 following vector functions. r₁(t) = (t², 13t 42, t²), r₂(t) = (11t - 30, t², 10t - 24) for t 20 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.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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If two objects travel through space along two different curves, it is often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) Their paths 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 following vector functions. r₁(t) = (t², 13t – 42, t²), r₂(t) = (11t — 30, t², 10t – 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.) t =
Transcribed Image Text:If two objects travel through space along two different curves, it is often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) Their paths 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 following vector functions. r₁(t) = (t², 13t – 42, t²), r₂(t) = (11t — 30, t², 10t – 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.) t =
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