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.

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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(b) In the second variation, the paper is still going to move due southeast at v2 mi/hr. But now the ant
is moving 2 mi/hr relative to the paper in a direction such that the ant travels due east relative to the
table. Find the direction of travel of the ant relative to the paper. Also find the speed of the ant relative
to the table.
Transcribed Image Text:(b) In the second variation, the paper is still going to move due southeast at v2 mi/hr. But now the ant is moving 2 mi/hr relative to the paper in a direction such that the ant travels due east relative to the table. Find the direction of travel of the ant relative to the paper. Also find the speed 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,
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
Transcribed Image Text: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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