6. A flying robot is programed to follow the following three-dimensional position function while navigating an open space with no wind. The displacements in x, y, and z are measured in meters and t in seconds. = 0.0560t* – 1.200t² + 2.300t + 0.3400 y(t) = 0.6700t3 – 1.570t² z(t) = 0.2200t³ x(t) (a) At t = 1.44 s, what angle does the robot's velocity vector, v, make with its acceleration vector, å? Os
6. A flying robot is programed to follow the following three-dimensional position function while navigating an open space with no wind. The displacements in x, y, and z are measured in meters and t in seconds. = 0.0560t* – 1.200t² + 2.300t + 0.3400 y(t) = 0.6700t3 – 1.570t² z(t) = 0.2200t³ x(t) (a) At t = 1.44 s, what angle does the robot's velocity vector, v, make with its acceleration vector, å? Os
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![6. A flying robot is programmed to follow the following three-dimensional position function while navigating an open space with no wind. The displacements in \( x, y, \) and \( z \) are measured in meters and \( t \) in seconds.
\[ x(t) = 0.0560t^4 - 1.200t^2 + 2.300t + 0.3400 \]
\[ y(t) = 0.6700t^3 - 1.570t^2 \]
\[ z(t) = 0.2200t^3 \]
**Graph:**
The image includes a 3D plot displaying the trajectory of the robot based on the given equations. The axes are labeled \( x(t) \), \( y(t) \), and \( z(t) \), showing the robot's path from \( 0 \leq t < 1.5 \) seconds. The graph illustrates how the robot moves through the 3D space based on the functions for each coordinate.
**Questions:**
(a) At \( t = 1.44 \) s, what angle does the robot’s velocity vector, \( \vec{v} \), make with its acceleration vector, \( \vec{a} \)?
(b) What is the dimensionless unit vector that is perpendicular to the plane formed by \( \vec{v} \) and \( \vec{a} \) at the moment that \( v_y = 0 \) m/s? This vector must have a negative x-component.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e7c4d7d-ede9-4b81-8e82-325ff8e9546c%2F9e350e15-271c-4e7e-8773-2aa82fd16083%2Fmcjthh_processed.png&w=3840&q=75)
Transcribed Image Text:6. A flying robot is programmed to follow the following three-dimensional position function while navigating an open space with no wind. The displacements in \( x, y, \) and \( z \) are measured in meters and \( t \) in seconds.
\[ x(t) = 0.0560t^4 - 1.200t^2 + 2.300t + 0.3400 \]
\[ y(t) = 0.6700t^3 - 1.570t^2 \]
\[ z(t) = 0.2200t^3 \]
**Graph:**
The image includes a 3D plot displaying the trajectory of the robot based on the given equations. The axes are labeled \( x(t) \), \( y(t) \), and \( z(t) \), showing the robot's path from \( 0 \leq t < 1.5 \) seconds. The graph illustrates how the robot moves through the 3D space based on the functions for each coordinate.
**Questions:**
(a) At \( t = 1.44 \) s, what angle does the robot’s velocity vector, \( \vec{v} \), make with its acceleration vector, \( \vec{a} \)?
(b) What is the dimensionless unit vector that is perpendicular to the plane formed by \( \vec{v} \) and \( \vec{a} \) at the moment that \( v_y = 0 \) m/s? This vector must have a negative x-component.
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