Question

Suppose you first walk 29.7 m in a direction 20 degrees east of north and then 21.7 m in a direction 40 degrees north of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position?

a) How far are you from your starting point

b) and what is the compass direction of a line connecting your starting point to your final position?

Answer 1

Answer on Question #80877 Physics / Other

Suppose you first walk $29.7\mathrm{m}$ in a direction 20 degrees east of north and then $21.7\mathrm{m}$ in a direction 40 degrees north of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position?

Solution:

The components of a displacement

$$s _ {x} = 2 9. 7 \sin 2 0 {}^ {\circ} - 2 1. 7 \cos 4 0 {}^ {\circ} = - 6. 4 7 \mathrm {k m}$$ $$s _ {y} = 2 9. 7 \cos 2 0 {}^ {\circ} + 2 1. 7 \sin 4 0 {}^ {\circ} = 4 1. 9 \mathrm {k m}$$

Therefore

(a) The absolute value of the displacement

$$s = \sqrt {s _ {x} ^ {2} + s _ {y} ^ {2}} = \sqrt {(- 6 . 4 7) ^ {2} + 4 1 . 9 ^ {2}} = 4 2. 4 \mathrm {k m}$$

(b) The direction

$$\tan \theta = \frac {s _ {y}}{s _ {x}} = \frac {4 1 . 9}{- 6 . 4 7} = - 6. 4 8, \quad \theta = 9 8. 8 {}^ {\circ}$$

or 81.2 degrees north of west.

Answers: $42.4\mathrm{km}$ ，81.2degrees north of west

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