Answer to Question #224659 in Physics for Gelo

Question

From your house you jog 10m in the direction of 25 degree north of east, then adter you changed your direction by 6m, 15 degree north of east. Graph and calculate the magnitude and angle of the resultant vector using analytical method.

Answer 1

10 m at 25° N of E:

$$d_{1N}=10\sin25°=4.23\text{ m},\\ d_{1E}=10\cos25°=9.06\text{ m}.$$

6 m at 15° N of E:

$$d_{2N}=6\sin15°=1.55\text{ m},\\ d_{2E}=6\cos15°=5.80\text{ m}.$$

The resultant vector components:

$$d_N=d_{1N}+d_{2N}=5.78\text{ m}.\\ d_E=d_{1E}+d_{2E}=14.9\text{ m}.\\ d=\sqrt{d_N^2+d_E^2}=15.9\text { m}.\\\space\\ \theta=\arctan{\frac{d_N}{d_E}} =21.2°.$$