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a nomad wanders 5km south, then 8km west, then 10km northeast. What is the resultant vector...

a nomad wanders 5km south, then 8km west, then 10km northeast. What is the resultant vector displacement of the nomad in component form?

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Answer #1

Consider the east-west direction along x-axis and north-south direction along y-axis

In unit vector notations, we can write each displacement as

= 0 i - 5 j

= - 8 i + 0 j

= (10 Cos45) i + (10 Sin45) j = 7.07 i + 7.07 j

Resultant displacement is given as

= + +

= (0 i - 5 j) + (- 8 i + 0 j) + (7.07 i + 7.07 j )

= - 0.93 i + 2.07 j

magnitude : sqrt((- 0.93)2 + (2.07)2) = 2.3 km

Direction : tan-1(2.07/0.93) = 65.85 deg south of east

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