Consider an object moving in the plane whose location at time t seconds is given by the parametric equations: x(t)=5cos(xt) y(t)=3sin(at). Assume the distance units in the plane are meters. (a) The object is moving around an ellipse with equation: + =1 where a= 5 and b= 3 (b) The location of the object at time t=1/3 seconds is 2.5 2.598 (c) The horizontal velocity of the object at time t is x' (t)=-5π sin(лt) (d) The horizontal velocity of the object at time t=1/3 seconds is (e) The vertical velocity of the object at time t is y' (t) = 3π cos(πt) m/s. m/s. m/s. (f) The vertical velocity of the object at time t=1/3 seconds is 4.712 m/s. (g) The slope of the tangent line at time t=1/3 seconds is -0.347 (h) Recall, the speed of the object at time t is given by the equation: s(t)=√√ [x '(t)]² + [y' (t)]² m/s. The speed of the object at time t=1/3 seconds is × (i) The first time when the horizontal and vertical velocities are equal is time t= 0.828 (j) Let Q be the position of the object at the time you found in part (i). The slope of the tangent line to the ellipse at Q is |
Consider an object moving in the plane whose location at time t seconds is given by the parametric equations: x(t)=5cos(xt) y(t)=3sin(at). Assume the distance units in the plane are meters. (a) The object is moving around an ellipse with equation: + =1 where a= 5 and b= 3 (b) The location of the object at time t=1/3 seconds is 2.5 2.598 (c) The horizontal velocity of the object at time t is x' (t)=-5π sin(лt) (d) The horizontal velocity of the object at time t=1/3 seconds is (e) The vertical velocity of the object at time t is y' (t) = 3π cos(πt) m/s. m/s. m/s. (f) The vertical velocity of the object at time t=1/3 seconds is 4.712 m/s. (g) The slope of the tangent line at time t=1/3 seconds is -0.347 (h) Recall, the speed of the object at time t is given by the equation: s(t)=√√ [x '(t)]² + [y' (t)]² m/s. The speed of the object at time t=1/3 seconds is × (i) The first time when the horizontal and vertical velocities are equal is time t= 0.828 (j) Let Q be the position of the object at the time you found in part (i). The slope of the tangent line to the ellipse at Q is |
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 12T
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Part D, H, J
![Consider an object moving in the plane whose location at time t seconds is given by the parametric equations:
x(t)=5cos(xt)
y(t)=3sin(at).
Assume the distance units in the plane are meters.
(a) The object is moving around an ellipse with equation:
+
=1
where a= 5
and b= 3
(b) The location of the object at time t=1/3 seconds is
2.5
2.598
(c) The horizontal velocity of the object at time t is x' (t)=-5π sin(лt)
(d) The horizontal velocity of the object at time t=1/3 seconds is
(e) The vertical velocity of the object at time t is y' (t) = 3π cos(πt)
m/s.
m/s.
m/s.
(f) The vertical velocity of the object at time t=1/3 seconds is 4.712
m/s.
(g) The slope of the tangent line at time t=1/3 seconds is -0.347
(h) Recall, the speed of the object at time t is given by the equation:
s(t)=√√ [x '(t)]² + [y' (t)]² m/s.
The speed of the object at time t=1/3 seconds is
×
(i) The first time when the horizontal and vertical velocities are equal is time t= 0.828
(j) Let Q be the position of the object at the time you found in part (i). The slope of the tangent line to the ellipse at Q is |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b80d742-db57-4c96-9c26-23084ccc0fb2%2F3483742b-1431-4911-ab73-7d9fee01a038%2F6idgjlp_processed.png&w=3840&q=75)
Transcribed Image Text:Consider an object moving in the plane whose location at time t seconds is given by the parametric equations:
x(t)=5cos(xt)
y(t)=3sin(at).
Assume the distance units in the plane are meters.
(a) The object is moving around an ellipse with equation:
+
=1
where a= 5
and b= 3
(b) The location of the object at time t=1/3 seconds is
2.5
2.598
(c) The horizontal velocity of the object at time t is x' (t)=-5π sin(лt)
(d) The horizontal velocity of the object at time t=1/3 seconds is
(e) The vertical velocity of the object at time t is y' (t) = 3π cos(πt)
m/s.
m/s.
m/s.
(f) The vertical velocity of the object at time t=1/3 seconds is 4.712
m/s.
(g) The slope of the tangent line at time t=1/3 seconds is -0.347
(h) Recall, the speed of the object at time t is given by the equation:
s(t)=√√ [x '(t)]² + [y' (t)]² m/s.
The speed of the object at time t=1/3 seconds is
×
(i) The first time when the horizontal and vertical velocities are equal is time t= 0.828
(j) Let Q be the position of the object at the time you found in part (i). The slope of the tangent line to the ellipse at Q is |
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