A hiker walks 20 Km towards the North, then 15 Km Southwards, then 10 Km Eastwards, and finally 12 Km at 30º due East. What is the hiker´s displacement?

Explanation:

We shall represent all displacements in vector form , in terms of i and j . I represents unit displacement towards east and j represents unit displacement in north direction .

First displacement D₁ = 20 j

second displacement D₂ = -15 j

Third displacement D₃ = 10 i

Fourth displacement D₄ = 12 cos30 i + 12 sin30 j  [ 12 cos 30 is displacement towards east and 12 sin30 is displacement towards north ]

Total displacement = 20 j - 15 j + 10 i + 12 cos30 i + 12 sin30 j

= 5 j + 10 i + 10.4 i + 6 j

= 20.4 i + 11 j

Magnitude of displacement = √ ( 20.4² + 11² )

= √ ( 416.16 + 121)

= √ 537.16

= 23.17 m

the answer is d. 4

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