High School

You walk 1.57 km north, then 0.846 km east.

Find the magnitude and the direction of your displacement vector, expressed as an angle relative to the northward direction.

Answer :

Final answer:

The magnitude of your displacement vector is approximately 1.783 km, and the direction is approximately 28.6 degrees relative to the northward direction.

Explanation:

To find the magnitude and direction of your displacement vector, we can use the Pythagorean theorem and trigonometric functions.

First, let's calculate the magnitude of the displacement vector:

Using the given information, you walked 1.57 km north and then 0.846 km east. We can represent these displacements as vectors:

  • Northward displacement vector: 1.57 km
  • Eastward displacement vector: 0.846 km

Now, we can use the Pythagorean theorem to find the magnitude of the displacement vector:

Magnitude = sqrt((1.57 km)^2 + (0.846 km)^2)

Magnitude = sqrt(2.4649 km^2 + 0.716116 km^2)

Magnitude = sqrt(3.1810169 km^2)

Magnitude ≈ 1.783 km

Next, let's determine the direction of the displacement vector relative to the northward direction:

We can use trigonometric functions to find the angle:

Tan(angle) = (0.846 km) / (1.57 km)

Angle = arctan(0.846 km / 1.57 km)

Angle ≈ 28.6 degrees

Therefore, the magnitude of your displacement vector is approximately 1.783 km, and the direction is approximately 28.6 degrees relative to the northward direction.

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