Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 10.3, Problem 42PS
To determine
To find: the value of
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Let r(t)
(15, cos t, -3 sin t) be the position vector of an object. Find the velocity
and speed of the object.
The position vector r describes the path of an object moving in the xy-plane.
Position Vector
Point
r(t) = 6 cos ti + 6 sin tj
(3V2, 3V2)
(a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object.
v(t) =
s(t)
a(t)
(b) Evaluate the velocity vector and acceleration vector of the object at the given point.
E) -
=
The vector function
r(t)
(1+2 cos t) i+ 3j+(5 – 2 sin t) k
traces out a circle in 3-space as t varies. De-
termine the radius and center of this circle.
Chapter 10 Solutions
Calculus
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- The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 2 cos ti + 2 sin tj (VZ, V2) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. a(#) =arrow_forwardFind the parametric equations for the line through the point(0, 1, 2) that is perpendicular to the line x = 1 + t, y = 1 − t, z = 2t, and intersects this line.arrow_forwardA fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: d→1 for 0.41 m southwest (that is, at 45° from directly south and from directly west), d→2 for 0.52 m due east, and d→3 for 0.77 m at 60° north of east. Let the positive x direction be east and the positive y direction be north. What are (a) the x component and (b) the y component of d→1? What are (c) the x component and (d) the y component of d→2? What are (e) the x component and (f) the y component of d→3? What are (g) the x component and (h) the y component, (i) the magnitude, and (j) the direction of the ant's net displacement? If the ant is to return directly to the starting point, (k) how far and (l) in what direction should it move? Give all angles as positive (counterclockwise) angles relative to the +x-axis.arrow_forward
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