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Luba_88 [7]
3 years ago
9

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 des

tination. 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
Mathematics
1 answer:
geniusboy [140]3 years ago
6 0

Answer:

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

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) <em>A group of hikers walks 3 miles east and then 1 mile north:</em>

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

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

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

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

\vec r = \vec r_{A}+\vec r_{B}  (1)

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

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

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

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