Let r(t) = (sin(2t), 3t, cos(2t)), t E [-T, "] be the position vector of a particle at time t. (a) Show that the velocity and acceleration vectors are always perpendicular. (b) Is there any time t for which r(t) and the velocity vector are perpendicular? Is so, find all such values of t.
Let r(t) = (sin(2t), 3t, cos(2t)), t E [-T, "] be the position vector of a particle at time t. (a) Show that the velocity and acceleration vectors are always perpendicular. (b) Is there any time t for which r(t) and the velocity vector are perpendicular? Is so, find all such values of t.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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![Let r(t) = (sin(2t), 3t, cos(2t)), t E [-n, 7] be the position vector of a particle
at time t.
(a) Show that the velocity and acceleration vectors are always perpendicular.
(b) Is there any time t for which r(t) and the velocity vector are perpendicular? Is so,
find all such values of t.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb18ac0ef-4d84-42fd-9d44-00456e05defd%2Ff75317a2-df46-4536-8f58-9cf5d1c59b2e%2F3fed72s_processed.png&w=3840&q=75)
Transcribed Image Text:Let r(t) = (sin(2t), 3t, cos(2t)), t E [-n, 7] be the position vector of a particle
at time t.
(a) Show that the velocity and acceleration vectors are always perpendicular.
(b) Is there any time t for which r(t) and the velocity vector are perpendicular? Is so,
find all such values of t.
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