Question

A hiker walks 500 m due notorth, 750 m due east, then 500 due north. What was the magnitude of her displacement and what was her distance covered?

Answer 1

The hiker's distance covered is 1750 meters and her displacement magnitude is 1250 meters northeastward.

Step-by-step explanation:

The student is asking about displacement and distance covered in a walking scenario involving vector addition. Displacement is a vector quantity that refers to the overall change in position, while distance is a scalar quantity that refers to how much ground is covered regardless of direction.

To determine the hiker's total displacement, we need to consider the vector sum of the individual displacements. The hiker first walks 500 m due north, then 750 m due east, and finally another 500 m due north. The total distance covered is the sum of these individual legs: 500 m + 750 m + 500 m, which equals 1750 m.

For the displacement, we add the vectors head-to-tail, resulting in a final displacement vector that starts at the hiker's original position and ends at the hiker's final position. We can find the magnitude of this displacement vector using the Pythagorean theorem since the walk is at right angles:

• North displacement: 500 m + 500 m = 1000 m
• East displacement: 750 m

The magnitude of the displacement (D) is then calculated as:

D = √((1000 m)^2 + (750 m)^2) = √(1000000 m^2 + 562500 m^2) = √(1562500 m^2) = 1250 m

So, the hiker's displacement magnitude is 1250 meters northeastward.