Question

Find the resultant displacement of a bear searching for berries on the mountain. The bear heads 55.0º north of west for 15.0 m; then it turns and heads to the west for another 7.00 m

Answer 1

Find the resultant displacement of a bear searching for berries on the mountain. The bear heads $55.0{}^{\circ}$ north of west for $15.0\mathrm{m}$; then it turns and heads to the west for another $7.00\mathrm{m}$

Displacement of the bear to north equals:

$$d _ {n} = 1 5 * \sin 5 5 {}^ {\circ} = 1 2. 2 9 m$$

Displacement of the bear to west equals:

$$d _ {w} = 1 5 * \cos 5 5 {}^ {\circ} + 7 = 1 5. 6 0 m$$

Therefore, the resultant displacement equals (using Pythagorean theorem):

$$d = \sqrt {d _ {n} ^ {2} + d _ {w} ^ {2}} = 1 9. 9 m$$

Answer: $19.9m$