Question

A hiker starts at his camp and moves the following distances while exploring his surroundings: 255 m east, 125 m at an angle 30.0° north of east, and 178 m at an angle 12.0° south of east. Find his resultant displacement from camp.

Answer 1

According to the following figure:

The coordinates of the displacement vectors will be:

$$\mathbf{d}_1 = (255,0)\space m\\ \mathbf{d}_2 = (125\cos30\degree ,125\sin30\degree) = (62.5\sqrt3 ,62.5)\space m\\ \mathbf{d}_3 = (178\cos12\degree ,-178\sin12\degree) \approx (174.11 ,-37.01)\space m\\$$

The resultant vector:

$$\mathbf{d} = \mathbf{d}_1 + \mathbf{d}_2 + \mathbf{d}_3=\\ =(255+62.5\sqrt3 +174.11, 0+62.5-37.01) \approx (537.36,25.49)\space m$$

Answer. $\mathbf{d} = (537.36,25.49)\space m$.