A person walks 8 km north, then 6 km south, and finally 2 km east. How far is he

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Question: A person walks 8 km north, then 6 km south, and finally 2 km east. How far is he from the starting point?

Options:

Correct Answer: 6 km

Solution:

He is 2 km north (8 km north - 6 km south) and 2 km east, so the distance is √(2^2 + 2^2) = √8 = 2√2 km, which is approximately 2.83 km.

A person walks 8 km north, then 6 km south, and finally 2 km east. How far is he from the starting point?

A person walks 8 km north, then 6 km south, and finally 2 km east. How far is he from the starting point?

Step 1: Start at the starting point.
Step 2: Walk 8 km north. Now you are 8 km north of the starting point.
Step 3: Walk 6 km south. Now you are 8 km - 6 km = 2 km north of the starting point.
Step 4: Walk 2 km east. Now you are still 2 km north and 2 km east of the starting point.
Step 5: To find the distance from the starting point, use the Pythagorean theorem: distance = √(north distance^2 + east distance^2).
Step 6: Plug in the values: distance = √(2^2 + 2^2) = √(4 + 4) = √8.
Step 7: Simplify √8 to get 2√2 km, which is approximately 2.83 km.

Vector Addition – Understanding how to combine movements in different directions to find the resultant position.
Pythagorean Theorem – Applying the theorem to calculate the distance from the starting point based on the final coordinates.