(a) What is t when the particle has height 6? t = 2 (b) What is the velocity of the particle when its height is 6? v = <0, pi, 3> (c) When the particle has height 6, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). Find a vector parametric equation for the position of the particle (in terms of the original parameter t) as it moves along this tangent line. L(t) = i +(pit)j + (6 + 3t) k
(a) What is t when the particle has height 6? t = 2 (b) What is the velocity of the particle when its height is 6? v = <0, pi, 3> (c) When the particle has height 6, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). Find a vector parametric equation for the position of the particle (in terms of the original parameter t) as it moves along this tangent line. L(t) = i +(pit)j + (6 + 3t) k
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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3. please solve it on paper
only part c is incorrect
Transcribed Image Text:Suppose r(t) = cos(πt)i + sin(πt)j + 3tk represents the position of a particle on a helix, where z is the height
of the particle.
(a) What is t when the particle has height 6?
t= 2
(b) What is the velocity of the particle when its height is 6?
<0, pi, 3>
=
(c) When the particle has height 6, it leaves the helix and moves along the tangent line at the constant velocity
found in part (b). Find a vector parametric equation for the position of the particle (in terms of the original
parameter t) as it moves along this tangent line.
L(t) = i i +(pit)j + (6 + 3t ) k
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