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Chapter 3: Problem 11

You walk west \(220 \mathrm{m},\) then north \(150 \mathrm{m} .\) What are the magnitude and direction of your displacement vector?

Short Answer

Expert verified
Using Pythagorean theorem the magnitude or distance of the displacement vector is approximately \(260\) m. Also using trigonometric rules the direction of displacement is approximately \(35°\) east of north or initially we get \(55°\) and after correcting the quadrant we get \(125°\) .

Step by step solution

01

Calculate the Magnitude

Here we have to use the concept of vectors in physics and Pythagorean theorem. The magnitude (distance) of a displacement vector can be found using Pythagorean theorem as \(\sqrt{{(220 \mathrm{m})^2 + (150 \mathrm{m})^2}}\). Calculate this value to find the magnitude of displacement.
02

Calculate the Direction

The direction of displacement can be calculated using trigonometric concepts. The angle of displacement, \(\theta\), is given by the expression \(\arctan\left(\frac{150\mathrm{m}}{220\mathrm{m}}\right)\). Calculate the value of this expression to find the direction of displacement in degrees.
03

Recognize the Quadrant

Taking into account the changes in the direction because of counters above, west and north indicates that we are in the second quadrant. So to find the true bearing we should subtract the angle found in Step 2 from \(180°\).

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Most popular questions from this chapter

A migrating whale follows the west coast of Mexico and North America toward its summer home in Alaska. It first travels \(360 \mathrm{km}\) northwest to just off the coast of northern California, and then turns due north and travels \(400 \mathrm{km}\) toward its destination. Determine graphically the magnitude and direction of its displacement.

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