Respuesta :
Answer:
Distance between Karl and Joe is 38.467 m
Solution:
Let us assume that you are at origin
Now, as per the question:
Joe's tent is 19 m away from yours in the direction [tex]19.0^{\circ}[/tex] north of east.
Now,
Using vector notation for Joe's location, we get:
[tex]\vec{r_{J}} = 19cos(19.0^{\circ})\hat{i} + 19sin(19.0^{\circ})\hat{j}[/tex]
[tex]\vec{r_{J}} = 17.96\hat{i} + 6.185\hat{j} m[/tex]
Now,
Karl's tent is 45 m away from yours and is in the direction [tex]39.0^{\circ}[/tex]south of east, i.e., [tex]- 39.0^{\circ}[/tex] from the positive x-axis:
Again, using vector notation for Karl's location, we get:
[tex]\vec{r_{K}} = 45cos(-319.0^{\circ})\hat{i} + 45sin(- 39.0^{\circ})\hat{j}[/tex]
[tex]\vec{r_{K}} = 34.97\hat{i} - 28.32\hat{j} m[/tex]
Now, obtain the vector difference between [tex]\vec{r_{J}}[/tex] and [tex]\vec{r_{K}}[/tex]:
[tex]\vec{r_{K}} - \vec{r_{J}} = 34.97\hat{i} - 28.32\hat{j} - (17.96\hat{i} + 6.185\hat{j}) m[/tex]
[tex]\vec{d} = \vec{r_{K}} - \vec{r_{J}} = 17.01\hat{i} - 34.51\hat{j} m[/tex]
Now, the distance between Karl and Joe, d:
|\vec{d}| = |17.01\hat{i} - 34.51\hat{j}|
[tex]d = \sqrt{(17.01)^{2} + (34.51)^{2}} m[/tex]
d = 38.469 m
The distance between Karl's and Joe's tent is:
