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 r:(t) = (t², 8t – 7, t2) r2(t) = (4t – 3, t², 10t – 9) for t > 0. Find the values oft 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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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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
r;(t) = (t2, 8t – 7, t2)
r2(t) = (4t – 3, t², 10t – 9)
-
-
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.)
Transcribed Image Text: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 r;(t) = (t2, 8t – 7, t2) r2(t) = (4t – 3, t², 10t – 9) - - 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.)
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