Answer to Question #139594 in Mechanics | Relativity for Zenjed

Question #139594
An airplane travels 209 km on a straight course at an angle of 22.5° east of north. It then changes course by moving 100 km north before reaching its destination. Determine the resultant displacement of the airplane
1
Expert's answer
2020-10-21T09:52:09-0400

the resulting displacement of the OB aircraft is determined by the cosine theorem

OB2=OA2+AB22OAABcos(180022.50)OB^2=OA^2+AB^2-2 \cdot OA \cdot AB \cdot \cos(180^0-22.5^0)

OB2=2092+10022209100cos(157.50)OB^2=209^2+100^2-2 \cdot 209 \cdot 100 \cdot \cos(157.5^0)

OB2=43681+100002209100(0.924)OB^2=43681+10000-2 \cdot 209 \cdot 100 \cdot (-0.924)

OB2=43681+10000+39877.2OB^2=43681+10000+39877.2

OB2=93558.2OB^2=93558.2

then

OB=93558.2=305.873kmOB=\sqrt{93558.2}=305.873km


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