The displacement refers to a change in the position. We know they walk 340 m to the West and 129 meters to the South. Let's draw the vectors. Also, the displacement is a vector.
To find the total displacement, we have to add the vectors. We'll use i for horizontal components and j for vertical components.
(a) The total displacement is
[tex]\vec{R}=(-340i-129j)m[/tex]The average speed refers to the quotient between the total distance traveled and the time elapsed.
[tex]\bar{v}=\frac{d_{total}}{t_{total}}=\frac{340m+129m}{14\min }[/tex]But, transform 14 minutes to seconds. Just multiply 14*60.
[tex]\bar{v}=\frac{469m}{14\cdot60\sec}=\frac{469m}{840\sec }\approx0.56(\frac{m}{s})[/tex](b) Their average speed is 0.56 (m/s).
At last, the average velocity refers to the total displacement divided by the time elapsed.
[tex]\begin{gathered} \vec{v}=\frac{\vec{R}}{t}=\frac{(-340i-129j)m}{840\sec }=(-\frac{340i}{840}-\frac{129j}{840})(\frac{m}{s}) \\ \vec{v}=(-0.40i-0.15j)(\frac{m}{s}) \end{gathered}[/tex](c) Their average velocity is (-0.40i-0.15j)(m/s)
