Question

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description the midterm exam covers material from chapters 1 - 5.
instructions from the list of choices, select the one best answer.
multiple attempts not allowed. this test can only be taken once.
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question 5 1 points save answer
a runaway dog walks 0.64 km due north. he then runs due west. if the magnitude of the dogs total displacement vector is 0.91 km, what is the magnitude of the dogs displacement vector in the due west direction?
0.33 km
0.41 km
0.27 km
0.65 km
0.52 km

Explanation:

Step1: Apply Pythagorean theorem

The displacement vectors form a right - triangle. Let \(d_{north}=0.64\) km (north - ward displacement) and \(d_{total} = 0.91\) km (total displacement). Let \(d_{west}\) be the west - ward displacement. By the Pythagorean theorem \(d_{total}^2=d_{north}^2 + d_{west}^2\). So, \(d_{west}^2=d_{total}^2 - d_{north}^2\).

Step2: Substitute values

Substitute \(d_{total}=0.91\) km and \(d_{north}=0.64\) km into the formula:

$$
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$$

Step3: Solve for \(d_{west}\)

Take the square root of \(d_{west}^2\): \(d_{west}=\sqrt{0.4185}\approx0.65\) km

Answer:

0.65 km