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Suppose that after t seconds, where t≥ 0, the trajectories of two particles are given by the vector functions r₁(t) = (t², 15-4t, 1²), r₂(t) = (4t-3,t(4-t), 2t+3) (a) At what point do the two particles collide? That is, at what point is r₁(t) = r₂(t) for the same value of t? (b) Find their angle of collision, correct to the nearest degree. (c) Do the two trajectories cross paths anywhere else? That is, is there s,t> 0 such that s t and r₁(t) = r₂(s)? If so, find all such points. If not, explain why not.

Suppose that after t seconds, where t≥ 0, the trajectories of two particles are given by the vector functions r₁(t) = (t², 15-4t, 1²), r₂(t) = (4t-3,t(4-t), 2t+3) (a) At what point do the two particles collide? That is, at what point is r₁(t) = r₂(t) for the same value of t? (b) Find their angle of collision, correct to the nearest degree. (c) Do the two trajectories cross paths anywhere else? That is, is there s,t> 0 such that s t and r₁(t) = r₂(s)? If so, find all such points. If not, explain why not.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that after t seconds, where t≥ 0, the trajectories of two particles are given by the vector functions ri(t) = (t², 15-4t, 1²), r₂(t) = (4t-3, t(4-t), 2t + 3) (a) At what point do the two particles collide? That is, at what point is r₁(t) = r₂(t) for the same value of t? (b) Find their angle of collision, correct to the nearest degree. (c) Do the two trajectories cross paths anywhere else? That is, is there s,t> 0 such that st and ri(t) = r₂(s)? If so, find all such points. If not, explain why not.
Transcribed Image Text:Suppose that after t seconds, where t≥ 0, the trajectories of two particles are given by the vector functions ri(t) = (t², 15-4t, 1²), r₂(t) = (4t-3, t(4-t), 2t + 3) (a) At what point do the two particles collide? That is, at what point is r₁(t) = r₂(t) for the same value of t? (b) Find their angle of collision, correct to the nearest degree. (c) Do the two trajectories cross paths anywhere else? That is, is there s,t> 0 such that st and ri(t) = r₂(s)? If so, find all such points. If not, explain why not.
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