Respuesta :
For the answer to the question above,
Ricardo goes a distance (magnitude) of 27, in a direction of 60 degrees W of N
Jane goes a magnitude of 16 in a direction 30 degrees S of W
How I would solve this is to imagine that the started at (0,0)
And their walking represents vectors.
Ricardo:
X-coordinate = -27sin60 = 27sqrt(3)/2 = 23.383
Y-coordinate = 27cos60 = 27/2 = 13.5
So, after he walks, he is at point (-23.383, 13.5)
Jane:
X-coordinate = -16cos(30) = 16sqrt(3)/2 = 13.856
Y-coordinate = -16sin(30) = 16/2 = 8
So, after she walks, she is at point (-13.856, -8)
So, you have 2 points.
Use the distance formula to find their distance apart
Sqrt((-23.383+13.856)^2+(13.5+8)^2) = 23.516m
To find the direction, simply find the slope of the two points, and take the arc-tangent.
The slope = -9.527/21.5 = -0.443
Take the tan^-1 of this, which is -23.899 degrees.
This basically translates to, Ricardo must walk 23.899 degrees E of S
They will be 23.518 m apart
Ricardo must walk 23.899 degrees East of South to get to Jane
Ricardo goes a distance (magnitude) of 27, in a direction of 60 degrees W of N
Jane goes a magnitude of 16 in a direction 30 degrees S of W
How I would solve this is to imagine that the started at (0,0)
And their walking represents vectors.
Ricardo:
X-coordinate = -27sin60 = 27sqrt(3)/2 = 23.383
Y-coordinate = 27cos60 = 27/2 = 13.5
So, after he walks, he is at point (-23.383, 13.5)
Jane:
X-coordinate = -16cos(30) = 16sqrt(3)/2 = 13.856
Y-coordinate = -16sin(30) = 16/2 = 8
So, after she walks, she is at point (-13.856, -8)
So, you have 2 points.
Use the distance formula to find their distance apart
Sqrt((-23.383+13.856)^2+(13.5+8)^2) = 23.516m
To find the direction, simply find the slope of the two points, and take the arc-tangent.
The slope = -9.527/21.5 = -0.443
Take the tan^-1 of this, which is -23.899 degrees.
This basically translates to, Ricardo must walk 23.899 degrees E of S
They will be 23.518 m apart
Ricardo must walk 23.899 degrees East of South to get to Jane
Answer:
Part a)
[tex]d = 24.5 m[/tex]
Part b)
[tex]\theta = 39.2 [/tex] degree East of South
Explanation:
Let they both are at origin initially
so here we will have final coordinates of both of them is given as
Ricardo walk 28 m in direction of 60 degree West of North
[tex]x_1 = -28 sin60[/tex]
[tex]x_1 = -24.2 m[/tex]
[tex]y_1 = 28 cos60[/tex]
[tex]y_1 = 14 m[/tex]
Jane walks 10 m in direction 30 degree South of West
[tex]x_2 = -10 cos30[/tex]
[tex]x_2 = -8.66 m[/tex]
[tex]y_2 = -10 sin30[/tex]
[tex]y_2 = -5 m[/tex]
Part a)
distance between them is given as
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]d = \sqrt{(-24.2 + 8.66)^2 + (14 + 5)^2}[/tex]
[tex]d = 24.5 m[/tex]
Part b)
direction of motion of Ricardo is given as
[tex]tan\theta = \frac{x_2 - x_1}{y_2 - y_1}[/tex]
[tex]tan\theta = \frac{24.2 - 8.66}{14 + 5}[/tex]
[tex]\theta = 39.2 [/tex] degree East of South
