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Joe has a date with Jill. Her house is 5 km east of his, but he has to do some things before he picks her up. He first heads 7 km N of his house to get flowers. He then travels 5 km east to pick up the movie tickets. Then he heads to her house. What was he distance? What was his displacement?

User Shikina
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Final answer:

Joe traveled a total distance of 17 km and his displacement is approximately 12.21 km northeast.

Step-by-step explanation:

Joe needs to calculate both the total distance he traveled as well as his displacement from his starting point to Jill's house. Distance is the total length of his journey, while displacement is the shortest path from the starting point to the endpoint, taking direction into account.

To find the total distance we add up all the distances traveled: 7 km north + 5 km east + 5 km east (to Jill's house), which equals 17 km. However, Joe's displacement requires us to consider only the straight-line distance from his starting point to Jill's house. Since Joe's house and Jill's house are 5 km apart eastwards, the 5 km he traveled east to get movie tickets does not change the resultant eastward displacement.

Therefore, Joe's displacement consists of two components: 7 km northward and 10 km eastward. By applying the Pythagorean theorem (since this forms a right-angled triangle), we calculate his displacement as √(7² + 10²) = √(49 + 100) = √149 ≈ 12.21 km northeast.

User Jen R
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