Question

Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 28.0 in a direction 60.0 west of north. Jane walks 10.0 in a direction 30.0 south of west. They then stop and turn to face each other
**What is the distance between them? **In what direction should Ricardo walk to go directly toward Jane?

Answer 1

Answer:

Part a)

$d = 24.5 m$

Part b)

$\theta = 39.2$ 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

$x_1 = -28 sin60$

$x_1 = -24.2 m$

$y_1 = 28 cos60$

$y_1 = 14 m$

Jane walks 10 m in direction 30 degree South of West

$x_2 = -10 cos30$

$x_2 = -8.66 m$

$y_2 = -10 sin30$

$y_2 = -5 m$

Part a)

distance between them is given as

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$d = \sqrt{(-24.2 + 8.66)^2 + (14 + 5)^2}$

$d = 24.5 m$

Part b)

direction of motion of Ricardo is given as

$tan\theta = \frac{x_2 - x_1}{y_2 - y_1}$

$tan\theta = \frac{24.2 - 8.66}{14 + 5}$

$\theta = 39.2$ degree East of South

Answer 2

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