Question

If you walk 6.00 m, N and 5.00 m E, what is your final location from your start? (magnitude, angle, and direction)

Answer 1

The final location from the start is 7.81 meters away at an angle of 38.66 degrees east of north.

Step-by-step explanation:

To find the final location from the starting point, we can use the Pythagorean theorem to calculate the magnitude of the displacement. Walking 6.00 meters north and 5.00 meters east creates a right-angled triangle. The displacement (d) can be calculated using \(d = \sqrt{(6.00 \, \text{m})^2 + (5.00 \, \text{m})^2}\), which gives us \(d = \sqrt{36 + 25} = \sqrt{61} \approx 7.81 \, \text{m}\).

Now, to determine the angle of this displacement, we can use trigonometry. The tangent of the angle (θ) is equal to the opposite side (5.00 m) divided by the adjacent side (6.00 m). Therefore, \(θ = \tan^{-1}\left(\frac{5.00 \, \text{m}}{6.00 \, \text{m}}\right) \approx 38.66^\circ\).

So, the final location is approximately 7.81 meters away from the starting point, at an angle of approximately 38.66 degrees east of north. This means if you draw a straight line from the starting point to the final location, the angle from north would be about 38.66 degrees in an eastward direction.

Answer 2

Your final location, considering a displacement of 6.00 m north and 5.00 m east, is 7.81 m in magnitude at an angle of 39.80° north of east.

Step-by-step explanation:

In order to determine the final location, we can use the Pythagorean theorem to find the magnitude of the displacement. The displacement in the north direction (Δy) is 6.00 m, and in the east direction (Δx) is 5.00 m. Using the formula
`\( √((\Delta x)^2 + (\Delta y)^2) \)`, we find the magnitude:

`\[ \sqrt{(5.00 \, \text{m})^2 + (6.00 \, \text{m})^2}` = 7.81 m

Now, to determine the angle of the displacement, we can use the tangent inverse function. The angle (θ) is given by
`\( \tan^(-1)\left((\Delta y)/(\Delta x)\right) \)`:

`\[ \tan^(-1)\left(\frac{6.00 \, \text{m}}{5.00 \, \text{m}}\right) = 39.80^\circ \]`

Therefore, the final location is 7.81 m in magnitude at an angle of 39.80° north of east. This means that if you walk 6.00 m north and 5.00 m east from your starting point, your final location is approximately 7.81 meters away, and the direction is 39.80° north of east. This vector representation accounts for both distance and direction, providing a comprehensive understanding of the overall displacement.