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Zha begins 7 kilometers to the north of town, and rides his bike along a straight trail which leads to a park 3 kilometers west of town. He takes 20 minutes to cover this distance. •Write a vector in component form describing Zha's bike ride. oFind the magnitude and direction of this vector. • Find the component of Zha's motion which is in the direction "southwest". (Use a unit vector to represent this direction.) Use both forms of the dot product (algebraic and geometric) to compute this, and compare to be sure you get the same answe both ways. ways. same answer both •Write parametric equations expressing Zha's motion, with town being represented by the origin, and t 0 representing his start point. oFind the coordinates of Zha's location after 5 minutes using these parametric equations. o Eliminate the parameter to get a Cartesian equation for this linear path. Verify algebraical that this equation represents this line. - Verify graphically using Desmos or other technology that the parametric equations and the Cartesian equation give the same line. Suppose Zha rides back along the same path, but now t 0 represents the new start point, which was the original end point. What changes in the parametrization? Does the Cartesian equation change? Explain.

Zha begins 7 kilometers to the north of town, and rides his bike along a straight trail which leads to a park 3 kilometers west of town. He takes 20 minutes to cover this distance. •Write a vector in component form describing Zha's bike ride. oFind the magnitude and direction of this vector. • Find the component of Zha's motion which is in the direction "southwest". (Use a unit vector to represent this direction.) Use both forms of the dot product (algebraic and geometric) to compute this, and compare to be sure you get the same answe both ways. ways. same answer both •Write parametric equations expressing Zha's motion, with town being represented by the origin, and t 0 representing his start point. oFind the coordinates of Zha's location after 5 minutes using these parametric equations. o Eliminate the parameter to get a Cartesian equation for this linear path. Verify algebraical that this equation represents this line. - Verify graphically using Desmos or other technology that the parametric equations and the Cartesian equation give the same line. Suppose Zha rides back along the same path, but now t 0 represents the new start point, which was the original end point. What changes in the parametrization? Does the Cartesian equation change? Explain.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 48E
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Zha begins 7 kilometers to the north of town, and rides his bike along a straight trail which leads to a park 3 kilometers west of town. He takes 20 minutes to cover this distance. •Write a vector in component form describing Zha's bike ride. oFind the magnitude and direction of this vector. • Find the component of Zha's motion which is in the direction "southwest". (Use a unit vector to represent this direction.) Use both forms of the dot product (algebraic and geometric) to compute this, and compare to be sure you get the same answe both ways. ways. same answer both •Write parametric equations expressing Zha's motion, with town being represented by the origin, and t 0 representing his start point. oFind the coordinates of Zha's location after 5 minutes using these parametric equations. o Eliminate the parameter to get a Cartesian equation for this linear path. Verify algebraical that this equation represents this line. - Verify graphically using Desmos or other technology that the parametric equations and the Cartesian equation give the same line. Suppose Zha rides back along the same path, but now t 0 represents the new start point, which was the original end point. What changes in the parametrization? Does the Cartesian equation change? Explain.
Transcribed Image Text:Zha begins 7 kilometers to the north of town, and rides his bike along a straight trail which leads to a park 3 kilometers west of town. He takes 20 minutes to cover this distance. •Write a vector in component form describing Zha's bike ride. oFind the magnitude and direction of this vector. • Find the component of Zha's motion which is in the direction "southwest". (Use a unit vector to represent this direction.) Use both forms of the dot product (algebraic and geometric) to compute this, and compare to be sure you get the same answe both ways. ways. same answer both •Write parametric equations expressing Zha's motion, with town being represented by the origin, and t 0 representing his start point. oFind the coordinates of Zha's location after 5 minutes using these parametric equations. o Eliminate the parameter to get a Cartesian equation for this linear path. Verify algebraical that this equation represents this line. - Verify graphically using Desmos or other technology that the parametric equations and the Cartesian equation give the same line. Suppose Zha rides back along the same path, but now t 0 represents the new start point, which was the original end point. What changes in the parametrization? Does the Cartesian equation change? Explain.
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