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 |
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 24E
Related questions
Question
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 |
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 4 images
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning