Question

with airplane cruising 30,000ft, the navigator indicates to the captain that the plane should continue travelling north for 500 km and then turn to a heading of 45.0° east of north for 200 km. what will be the resultant distance traveled?

Answer 1

The distance travel by the airplane in heading toward north

$d_1=500km$

The distance travel by the airplane in heading 45$\degree$ east of north

$d_2=200km$

Resultant Distance travelled is given by

=$\sqrt{d_1^2+d_2^2+2d_2d_2cos 45\degree}$

=$\sqrt{500^2+200^2+2\times 500\times 200\times \dfrac{1}{\sqrt{2}}}$

=$\sqrt{250000+40000+141400}$

=$\sqrt{431400}=656.81km$

Hence The resultant distance is 656.81km