A hiker walks 1 km east, 2km north, 4 km east, then 6 km north. What is the distance and displacement of the hiker

The distance the hiker walked is, d = 13 km

The displacement of the hiker is, S = 9.4 km

Explanation:

Given data,

The displacement of towards east, d₁ = 1 km

The displacement of towards north, d₂ = 2 km

The displacement of towards east, d₃ = 4 km

The displacement of towards north, d₄ = 6 km

The total distance the hiker walked

d = d₁ + d₂ + d₃ + d₄

= 1 + 2 + 4 + 6

= 13 km

The distance the hiker walked is, d = 13 km

The resultant displacement of the hiker, S

S = √ (A² + B² + 2 A B cosФ)

Where,

A = d₁ + d₃ = 5 km

B = d₂ + d₄ = 8 km

Ф = angle between A and B = 90°

Substituting in the displacement equation

S = √ (5² + 8²)

= 9.4 km

Hence, the displacement of the hiker is, S = 9.4 km