Question

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

Answer 1

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

$OB^2=OA^2+AB^2-2 \cdot OA \cdot AB \cdot \cos(180^0-22.5^0)$

$OB^2=209^2+100^2-2 \cdot 209 \cdot 100 \cdot \cos(157.5^0)$

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

$OB^2=43681+10000+39877.2$

$OB^2=93558.2$

then

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