A man walks 3 km north, then 4 km west. What is his final position relative to t

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Question: A man walks 3 km north, then 4 km west. What is his final position relative to the starting point?

Options:

Correct Answer: 5 km North-West

Solution:

The distance from the starting point is √(3² + 4²) = 5 km in the north-west direction.

A man walks 3 km north, then 4 km west. What is his final position relative to the starting point?

A man walks 3 km north, then 4 km west. What is his final position relative to the starting point?

Step 1: Start at the initial position, which we can call point A.
Step 2: Walk 3 km north from point A to point B.
Step 3: From point B, walk 4 km west to point C.
Step 4: Now, we need to find the distance from point A to point C.
Step 5: Use the Pythagorean theorem, which states that the distance (d) can be calculated using the formula d = √(a² + b²), where a and b are the distances walked in the north and west directions.
Step 6: Substitute the values: a = 3 km (north) and b = 4 km (west).
Step 7: Calculate: d = √(3² + 4²) = √(9 + 16) = √25 = 5 km.
Step 8: The final position is 5 km from the starting point in the north-west direction.

Pythagorean Theorem – The relationship between the sides of a right triangle, used to calculate the distance from the starting point.
Vector Addition – Understanding how to combine movements in different directions to find a resultant position.