Question

a person walks 25 m east and then walks 31 m at an angle of 36 degrees north of east. what is the magnitude of the total displacement?

Answer 1

We will have:

So, the magnitude of the total displacement is:

$$\begin{array}{l} d = \sqrt {2 5 ^ {2} + 3 1 ^ {2} - 2 \cdot 2 5 \cdot 3 1 \cdot \cos (1 8 0 {}^ {\circ} - 3 6 {}^ {\circ})} = \\ = \sqrt {2 5 ^ {2} + 3 1 ^ {2} - 2 \cdot 2 5 \cdot 3 1 \cdot \cos (1 4 4 {}^ {\circ})} = 5 3. 3 \mathrm {m}. \\ \end{array}$$

Answer: 53.3 meters.