Respuesta :
Answer:
Step-by-step explanation:
Given
Plane travels 240 miles [tex]10^{\circ}[/tex] East of North
Position vector [tex]\vec{r_1}=240(\cos(10)\hat{j}+\sin (10)\hat{i})[/tex]
Then the plane travels 180 miles [tex]67^{\circ}[/tex] East of North
[tex]\vec{r_{21}}=180(\cos(67)\hat{j}+\sin (67)\hat{i})[/tex]
[tex]\vec{r_2}=\vec{r_{21}}+\vec{r_1}[/tex]
[tex]\vec{r_2}=\left ( 240\sin (10)+180\sin (67)\right )\hat{i}+\left ( 240\cos (10)+180\cos (67)\right )\hat{j}[/tex]
[tex]\vec{r_2}=\left ( 207.36\right )\hat{i}+\left ( 306.68\right )\hat{j}[/tex]
Total distance traveled in North direction is given by coefficient of \hat{j}
i.e. North[tex]=306.68\ miles\approx 307\ miles[/tex]
Total distance traveled in East direction is given by coefficient of \hat{i}
East [tex]=207.36\ miles\approx 207\ miles[/tex]
