Question

Repeat Exercise using analytical techniques, but reverse the order of the two legs of the walk and show that you get the same final result. (This problem shows that adding them in reverse order gives the same result—that is, $\mathit{B}\mathbf{+}\mathit{A}\mathbf{=}\mathit{A}\mathbf{+}\mathit{B}$.) Discuss how taking another path to reach the same point might help to overcome an obstacle blocking you other path.

Short answer

The distance from the starting point is ,$30.8m$ and the compass direction of a line connecting starting point to the final position is $35.8°$west of north.

Step-by-step solution

Triangle law of vector addition

The magnitude of the resultant vector is always in reverse order when two vectors are obtained along the two sides of a triangle.

Vector representation

The vector representation of vectors and by reversing the order is represented as

Fig: Vector representation

Magnitude of resultant vector

The magnitude of the resultant vector is

$R=\sqrt{A^2+B^2}$

Here$A$is the magnitude of the vector$A$(displacement towards west), and$B$is the magnitude of the vector$B$ (displacement towards north).

Substitute $18.0m$for $A$ and $25.0m$for $B$.

Direction of compass

The direction of the compass is

$\varnothing ={\tan }^{-1}\left(\frac{A}{B}\right)$

Substitute role="math" localid="1668685940044" $18.0m$for $A$and $25.0m$for.$B$

$$\begin{gathered} \varnothing ={\tan }^{-1}\left(\frac{18.0m}{25.0m}\right) \\ =35.8° \end{gathered}$$

Hence, the distance from the starting point is $30.8m$and the compass direction of a line connecting starting point to the final position is$35.8°$ west of north.