Answer:
The distance the hiker walked is, d = 13 km
The displacement of the hiker is, S = 9.4 km
Step-by-step 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