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.

Consider the equations xt=0.0560t4-1.200t2+2.300t+0.3400yt=0.6700t3-1.570t2zt=0.2200t3 Differentiate…

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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

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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