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.
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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Transcribed Image Text:(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.
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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