Respuesta :
Answer:
Sammy's course is 3.19 mph at a heading of 322.36°
Step-by-step explanation:
To solve this problem we need to calculate a sum of vectors.
We can calculate this sum decomposing both vectors in their horizontal and vertical component, and then we sum the components:
First vector: module 5, direction 310°
[tex]horizontal\ component: 5 * cos(310) = 3.2139[/tex]
[tex]vertical\ component: 5 * sin(310) = -3.8302[/tex]
Second vector: module 2, direction 110°
[tex]horizontal\ component: 2 * cos(110) = -0.6840[/tex]
[tex]vertical\ component: 2 * sin(110) = 1.8794[/tex]
Resultant vector:
[tex]horizontal\ component: 3.2139 - 0.6840 = 2.5299[/tex]
[tex]vertical\ component: -3.8302 + 1.8794 = -1.9508[/tex]
Now, to go back to the polar form, we can use the following procedure:
[tex]module = \sqrt{horizontal\ component^2 + vertical\ component^2 }[/tex]
[tex]module = \sqrt{2.5299^2 + (-1.9508)^2 }[/tex]
[tex]module = 3.1947[/tex]
[tex]angle = arc tangent(vertical\ component / horizontal\ component)[/tex]
[tex]angle = arc tangent(-1.9508 / 2.5299)[/tex]
[tex]angle = 322.36\°[/tex]
So Sammy's course is 3.19 mph at a heading of 322.36°
