Question

A plane travels 240 miles on a bearing of N 10° E and then changes its course to N 67° E and travels another 180 miles. Find the total distance traveled north and the total distance traveled east. (Round each answer to the nearest whole number.)

Answer 1

Answer:

Step-by-step explanation:

Given

Plane travels 240 miles $10^{\circ}$ East of North

Position vector $\vec{r_1}=240(\cos(10)\hat{j}+\sin (10)\hat{i})$

Then the plane travels 180 miles $67^{\circ}$ East of North

$\vec{r_{21}}=180(\cos(67)\hat{j}+\sin (67)\hat{i})$

$\vec{r_2}=\vec{r_{21}}+\vec{r_1}$

$\vec{r_2}=\left ( 240\sin (10)+180\sin (67)\right )\hat{i}+\left ( 240\cos (10)+180\cos (67)\right )\hat{j}$

$\vec{r_2}=\left ( 207.36\right )\hat{i}+\left ( 306.68\right )\hat{j}$

Total distance traveled in North direction is given by coefficient of \hat{j}

i.e. North$=306.68\ miles\approx 307\ miles$

Total distance traveled in East direction is given by coefficient of \hat{i}

East $=207.36\ miles\approx 207\ miles$