Question

Martha travels 3.5 km south and then 2 km west. What is the magnitude of Martha's displacement?

a) 5.5 km
b) 4.5 km
c) 2.5 km
d) 1.5 km

Answer 1

Martha's displacement is calculated using the Pythagorean theorem, applicable for right-angled triangles formed by her south and west travel. The calculation yields a displacement of 4.03 km, essentially closest to 4.5 km (option b).

Step-by-step explanation:

To find Martha's displacement, we use the Pythagorean theorem since her movement is along two perpendicular directions – south and west. Her displacement is the magnitude of the resultant vector that is formed by these two movements.

The formula for the magnitude of displacement is:

√(x2 + y2)

Where:

• x = 3.5 km (travel south, consider it as negative or positive depending on the convention)
• y = 2 km (travel west, consider it as negative or positive depending on the convention)

Substituting Martha's movements into the equation:

√(3.52 + 22)

= √(12.25 + 4)

= √(16.25)

= 4.03 km

So, Martha's displacement is 4.03 km which is closest to option (b) 4.5 km.