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

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

Answer 2

Part a)

`d = 24.5 m`

Part b)

`\theta = 39.2` degree East of South

Step-by-step 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 = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

`d = √((-24.2 + 8.66)^2 + (14 + 5)^2)`

`d = 24.5 m`

Part b)

direction of motion of Ricardo is given as

`tan\theta = (x_2 - x_1)/(y_2 - y_1)`

`tan\theta = (24.2 - 8.66)/(14 + 5)`

`\theta = 39.2` degree East of South