Question

Suppose you walk 12.5m in a direction exactly 23 degrees south of west then you walk 21m in a direction exactly 44 degrees west of north
for part A (I got) was The resultant, 28.03 meters
Now part b says:

What is the angle of the compass direction of a line connecting your starting point to your final position measured North of West in degress?

Answer 1

Answer on Question#58050 - Physics - Relativity

Suppose you walk $12.5\mathrm{m}$ a direction exactly 23 degrees south of west then you walk $21\mathrm{m}$ in a direction exactly 44 degrees west of north.

For part A (I got) was The resultant, 28.03 meters

Now part b says:

What is the angle of the compass direction of a line connecting your starting point to your final position measured North of West in degress?

Solution.

Draw the resulting position using vectors.

the starting point.

- final point.

According to the problem $\alpha_{1} = 23^{0}$ and $\alpha_{2} = 44^{0}$ .

Find components of displacement using the algebraic method of vector addition. The first vector has component $12.5\cos 23^0 \approx 11.5063$ directed to the south and $12.5\sin 23^0 \approx 4.8841$ directed to the west. The second vector has component $21\cos 44^0 \approx 15.1061$ directed to the west and $21\sin 44^0 \approx 14.5878$ directed to the north. Hence, the components of the displacement vector equal

$21\sin 44^{0} - 12.5\cos 23^{0} = 14.5878 - 11.5063 = 3.0815$ directed to the north

$12.5\sin 23^{0} + 21\cos 44^{0} = 4.8841 + 15.1061 = 19.9902$ directed to the west

Magnitude of vector for the Pythagorean theorem

$$d = \sqrt {3 . 0 8 1 5 ^ {2} + 1 9 . 9 9 0 2 ^ {2}} \approx 2 0. 2 2$$

$\varphi$ – the angle of the compass direction of a line connecting your starting point to your final position measured North of West. Using right triangle will get

$$\sin \varphi = \frac {19,9902}{20,22} \rightarrow \varphi = 81{}^{\circ}21'$$

Answer: $\varphi = 81{}^{\circ}21'$.

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