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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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 31E
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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
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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