A group of hikers walks 3 miles east and then 1 mile north. After taking a break, they then hike 4 miles east to their final destination. What vector describes their hike from their starting position to their final destination? Let 1 unit represent 1 mile. The vector that describes their hike from their starting position to their final destination is

Answer:

The vector that describes their hike from their starting position to their final destination is [tex]\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi][/tex].

Step-by-step explanation:

In this problem we assume that orthogonal axes coincide with the north and east. We proceed to translate each sentence from statement into vectorial equations:

(i) A group of hikers walks 3 miles east and then 1 mile north:

[tex]\vec r_{A} = 3\,\hat{i}+1\,\hat{j}\,\,\,[mi][/tex]

(ii) After taking a break, they then hike 4 miles east to their final destination:

[tex]\vec r_{B} = 4\,\hat{i}\,\,\,[mi][/tex]

The vector that describes their hike from their starting position to their final destination is the sum of the vectors deducted above. That is:

[tex]\vec r = \vec r_{A}+\vec r_{B}[/tex]  (1)

[tex]\vec r = (3\,\hat{i}+1\,\hat{j})+4\,\hat{i}\,\,\,[mi][/tex]

[tex]\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi][/tex]

The vector that describes their hike from their starting position to their final destination is [tex]\vec r = 7\,\hat{i}+1\,\hat{j}\,\,\,[mi][/tex].

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