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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