Question

A pilot flies in a straight path for 2 hours. He then makes a course correction, heading 15 degrees to the right of his original course and flies 1 hour in the new direction. If he maintains a constant speed of 575 miles per hour, how far is he from his starting position?

Answer 1

Answer:1711.8 miles

Explanation:

Given

Pilot flies for 2 hr in straight line with speed of 575 mph

and deviates 15 right from its path

Considering Plane flies towards east

Position vector of pilot after 2 hr

$\vec{r_1}=575\times 2\hat{i}$

After 1 hr

$\vec{r_{21}}=575\times 1\left ( cos15\hat{i}-sin(15)\hat{j}\right )$

$\vec{r_2}=\vec{r_{21}}+\vec{r_{1}}$

$\vec{r_2}=575\times 1\left ( cos15\hat{i}-sin(15)\hat{j}\right )+575\times 2\hat{i}$

$\vec{r_2}=1705.4\hat{i}-148.82\hat{j}$

Distance from original position is given by magnitude of $|r_2|$

$|r_2|=\sqrt{2930536.55}=1711.881$ miles