Question

Michael walks 10m north, 3m west, 5m south, 12m east, and then stops to catch his breath. What is the magnitude of his displacement from his original point? (Ans: Approx. 10 m)

Answer 1

Answer:

Answer is √(5² + 9²) = 10.29m

Explanation:

Let North be positive Y axis, then East is positive X-axis, West is negative x-axis and South is negative Y-axis.

Let the coordinates of original point be (0,0)

Then after moving 10m North, the coordinates as (0,10)

after moving 3m West, the coordinates are (-3,10)

then 5m South, the coordinates will be (-3,5)

and finally moving 12m East the final coordinates will be (9,5)

So the displacement from original point is the distance between (0,0) and (9,5) which can be calculated from distance formula i.e.

d= √[(9-0)² + (5-0)²] = √(9² + 5²) = √(81+25) = √106 = 10.29

Thus the displacement from original point is 10.29m