(a) In the first variation, we want to find the velocity vector for the ant relative to the paper that wouldresult in the ant traveling due east at 2 miles per hour relative to the table. The paper is still going tomove due southeast at v2 mi/hr. An ant walks due east at a constant speed of 2 mi/hr on a sheet of paper that rests on a table. Suddenly,the sheet of paper starts moving due southeast at v2 mi/hr. The following is a correct solution for findingthe resultant speed and direction of the ant relative to the table.Set up a coordinate system so that the positive y-axis corresponds to north and the positive x-axis correspondsto east. Then the velocity vector for the ant relative to the paper is given by (2,0). The velocity vector forthe paper relative to the table is given by (v2 cos (-4), v2 sin (-5))= (1, –1).Therefore, the resultant velocity vector is given by (2,0) + (1, –1) = (3, –1). The speed of the ant relativeto the table is v32 + 1² = v10 mi/hr and the direction the ant is traveling relative to the table is found by(금)using tan 0 =-1where 0 represents the angle made with the positive r-axis. In this case 0 = arctan33

An ant walks due east at a constant speed of 2 mi/hr on a sheet of paper that rests on a table. Suddenly, he sheet of paper starts moving due southeast at v2 mi/hr. The following is a correct solution for finding he resultant speed and direction of the ant relative to the table.

An ant walks due east at a constant speed of 2 mi/hr on a sheet of paper that rests on a table. Suddenly, he sheet of paper starts moving due southeast at v2 mi/hr. The following is a correct solution for finding he resultant speed and direction of the ant relative to the table.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 13CR

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

(a) In the first variation, we want to find the velocity vector for the ant relative to the paper that would
result in the ant traveling due east at 2 miles per hour relative to the table. The paper is still going to
move due southeast at v2 mi/hr.

An ant walks due east at a constant speed of 2 mi/hr on a sheet of paper that rests on a table. Suddenly,
the sheet of paper starts moving due southeast at v2 mi/hr. The following is a correct solution for finding
the resultant speed and direction of the ant relative to the table.
Set up a coordinate system so that the positive y-axis corresponds to north and the positive x-axis corresponds
to east. Then the velocity vector for the ant relative to the paper is given by (2,0). The velocity vector for
the paper relative to the table is given by (v2 cos (-4), v2 sin (-5))= (1, –1).
Therefore, the resultant velocity vector is given by (2,0) + (1, –1) = (3, –1). The speed of the ant relative
to the table is v32 + 1² = v10 mi/hr and the direction the ant is traveling relative to the table is found by
(금)
using tan 0 =
-1
where 0 represents the angle made with the positive r-axis. In this case 0 = arctan
3
3

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