Respuesta :
The distance between Ricardo and Jane :
a) 24.33 m of distance.
b) 34.55° east of the south.
Evaluating the equation given :
Now that we all know what we need to do in this question, let's head for each part of the problem.
a) Distance between Ricardo and Jane
In this case, we'd like to analyze the given data:
Ricardo (which we'll call R) is 28 m from the starting point at 60° west of north, and Jane (J) is 13 m at 30° south of west. therefore the distance between them, are going to be the point where they both stop and face each other.
Let's call the space between them as "D", to urge the distance of D, consistent with the picture will be:
D = J - R (1)
However, as they're facing in different angles and directions, we cannot do the difference of their values distance a bit like that. so as to do that, we'd like to calculate the components in the "x" and "y" axis of each vector. therein way, we will get the components of x and y of the Distance D, and then, the full distance between them will be:
D = √Dx² + Dy² (2)
So, let's get the components of x and y of R and J.
For Ricardo (R):
Rx = R sin60° = 28 sin60°
= -24.25 m
Ry = R cos60° = 28 cos60°
= 14 m
The sign "-" it's because R it's on the second quadrant, therefore in x, we'll need to add the negative.
For Jane (J):
Jx = J cos30° = 13 cos30°
= -10.39 m
Jy = J sin30° = 13 sin30°
= -6.5 m
Again, the negative is added because J is on the third quadrant.
Now that we've the components, let's calculate vector D using expression (1):
Dx = -10.39 - (-24.25) = 13.86 m
Dy = -6.5 - 14 = -20.5 m
Now, using expression (2) we will finally know the distance between Jane And Ricardo:
D = √(-20)² + (13.86)²
D = 24.33 m
This is the distance between Jane and Ricardo.
b) Direction of Ricardo walking to Jane
In this case, we have already got the components of x and y of the distance between them, so, to understand the direction:
Tanα = Dy/Dx
α = tan⁻¹ (Dy/Dx)
Replacing the values we have:
α = tan⁻¹ (-20/13.86)
α = 55.45°
Which should south of east or:
β = 90 - 55.45
β = 34.55°
Ricardo should walk 34.55° east of south
The question is incomplete. the full exercise is the following:
"Ricardo and Jane are standing under a tree within the middle of a pasture. An argument ensues, and that they walk away in different directions. Ricardo walks 28.0 m during a direction 60.0° west of north. Jane walks 12.0 m during a direction 30.0° south of west. They then stop and switch to face each other.
(a) what's the distance between them?
(b) In what direction should Ricardo walk to travel directly toward Jane?"
Learn more about directions at different angles :
brainly.com/question/2598206
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