A cyclist travels 100 m north and then 100 m east. What is the magnitude of the

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Question: A cyclist travels 100 m north and then 100 m east. What is the magnitude of the displacement from the starting point?

Options:

Correct Answer: 141.4 m

Solution:

Displacement = √(100² + 100²) = √20000 = 141.4 m.

A cyclist travels 100 m north and then 100 m east. What is the magnitude of the displacement from the starting point?

A cyclist travels 100 m north and then 100 m east. What is the magnitude of the displacement from the starting point?

Correct Answer: 141.4 m

Step 1: Understand that displacement is the shortest distance from the starting point to the ending point.
Step 2: Visualize the cyclist's path: they go 100 m north and then 100 m east, forming a right triangle.
Step 3: Identify the two sides of the triangle: one side is 100 m (north) and the other side is 100 m (east).
Step 4: Use the Pythagorean theorem to find the hypotenuse (displacement). The formula is: Displacement = √(side1² + side2²).
Step 5: Substitute the values into the formula: Displacement = √(100² + 100²).
Step 6: Calculate the squares: 100² = 10000, so Displacement = √(10000 + 10000).
Step 7: Add the squares: 10000 + 10000 = 20000.
Step 8: Take the square root: Displacement = √20000.
Step 9: Calculate the square root: √20000 = 141.4 m.

Displacement – Displacement is the shortest distance from the initial to the final position, represented as a vector.
Pythagorean Theorem – Used to calculate the magnitude of displacement when movement occurs in perpendicular directions.