Question

An airplane flies northwest for 250 mi and then west for 150 mi. What is the resultant displacement of the plane after this time?

Answer 1

Answer:371.564 mi

Explanation:

Given

Airplane flies northwest for 250 mi and then travels west 150 mi

That is first it travels 250cos45 in - ve x direction and simultaneously 250sin45 in y direction

after that it travels 150 mi in -ve x direction

So its position vector is given by

$r=-250cos45\hat{i}-150\hat{i}+250sin45\hat{j}$

$r=-\left ( 250cos45+150\right )\hat{i}+250sin45\hat{j}$

so magnitude of displacement is

$|r|=\sqrt{\left ( \frac{250}{\sqrt{2}}+150\right )^2+\left ( \frac{250}{\sqrt{2}}\right )^2}$

|r|=371.564 mi