49. If two objects travel through space along two different curves, it's often important to know whether they will col- lide. (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 150 r₁(t) = (t², 7t for t≥ 0. Do the particles - 12, t²) r₂(t) = (4t-3, t², 5t - 6) collide?
49. If two objects travel through space along two different curves, it's often important to know whether they will col- lide. (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 150 r₁(t) = (t², 7t for t≥ 0. Do the particles - 12, t²) r₂(t) = (4t-3, t², 5t - 6) collide?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
49
Transcribed Image Text:Then find para
equations and a computer to graph the curve.
48. Try to sketch by hand the curve of intersection of the
parabolic cylinder y = x² and the top half of the ellipsoid
x² + 4y² + 4z² = 16. Then find parametric equations for
this curve and use these equations and a computer to graph
the curve.
49. If two objects travel through space along two different
curves, it's often important to know whether they will col-
lide. (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) = (t², 7t - 12, t²)
for t≥ 0. Do the particles collide?
50. Two particles travel along the space curves
r₂(t) = (4t-3, t², 5t - 6)
10
r₂(t) = (1 + 2t, 1 + 6t, 1 + 14t)
r₁(t) = (t, t², t³)
Do the particles collide? Do their paths intersect?
13.2 Derivatives and Integrals of Vector Fun-
Later in this chapter we are
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