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2 years ago

If a person walks first 70 m in the direction 37° north of east, and then walks 82 m in the

Physics

1 answer:

Mrac [35]2 years ago

5 0

a. Aster is 56.3 m at 3.16° north-east from her initial position

b. She has to head to 183.16° or 86.84° south of west to return to her initial position

<h3>a. How to calculate how far Aster's final position from her initial position?</h3>

Let Aster's initial position be represented by the vector r = 0i + 0j

Since she then walks walks first 70 m in the direction 37° north of east, let this displacement be represented by the vector u = (70sin37°)i + (70cos37°)j

= (70 0.6018)i + (70 0.7986)j

= 42.13i + 55.9j

Also, she then walks 82 m in the direction 20° south of east. Let this displacement be represented by the vector v = (82sin20°)i - (82cos20°)j

= -(82 0.3420)i + (82 0.9397)j

= 28.05i - 77.05j

Finally, she walks 28 m in the direction 30° west of north. Let this displacement be represented by the vector, w = -(28sin30°)i + (28cos30°)j = -(28 0.5)i + (28 0.8660)j

= -14i + 24.25j m

So, the total displacement is R = r + u + v + w

= 42.13i + 55.9j + 28.05i + (-77.05)j + (-14)i + 24.25j m

= 56.18i + 3.1j

So, how far she walks is the magnitude of R. The magnitude of a vector Z = xi + yj is Z = √(x² + y²)

So, the magnitude of R = √((56.18)² + (3.1)²)

= √(3156.19 + 9.61)

= √3165.8

= 56.3 m

<h3>Her direction from final position to initial position</h3>

The direction of a vector Z = xi + yj is given by Ф = tan⁻¹ (y/x)

So, the direction of R is Ф' = tan⁻¹ (3.1/56.18)

= tan⁻¹ (0.0552)

= 3.16°

So, Aster is 56.3 m at 3.16° north-east from her initial position

<h3>b. What direction would she has to head to return to her initial position?</h3>

To return to her original position, the displacement vector is V = r - R

= 0i + 0j - (56.18i + 3.1j)

= -56.18i - 3.1j

So, the direction of V is Ф" = tan⁻¹ (-3.1/-56.18)

= tan⁻¹ (0.0552)

= 3.16°

Since this is in the third quadrant, we have that the direction she must go to return to her original position is α = 180° + 3.16°

= 183.16°

or 90° - 3.16°

= 86.84° south of west

So, she has to head to 183.16° or 86.84° south of west to return to her initial position

Learn more about direction of a vector here:

brainly.com/question/27854247

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