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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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