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 26.0 m in a direction 60.0∘ west of north. Jane walks 16.0 m in a direction 30.0∘ south of west. They then stop and turn to face each other. a. What is the distance between them? b. In what direction should Ricardo walk to go directly toward Jane?

Answer 1

Answer:

a)     d = 30.79 m , b) θ = -22.4° ,   θ = 22.4 South of East

Explanation:

The easiest way to solve problems with vectors is to use their components, for this the East-West direction coincides with the x-axis and the North-South direction coincides with the y-axis

Let's use the index for / Ricardo and the index for Jane, let's break down the displacements

Richard

X axis

      x₁ = 26.0 sin (60)

      x₁ = -22.52 m

Y Axis  

     y₁ = 26.0 cos 60

     y₁ = 13 m / s

Jane

X axis

       x₂ = 16.0 cos (180 +30)

       x₂ = -13.85 m

Y Axis  

        y₂ = 16.0 sin (180 + 30)

        y₂ = - 8.0 m

Now we can use Pythagoras' theorem to find the distance between them

         d = √ [(x₂ -x₁)² + (y₂ -y₁)²]

         d = √ [(-13.85 + 22.52)² + (-8 -13)²]

         d = 30.79 m

Let's use trigonometry to enter the address

         tan θ = Δy / Δx

         θ = tan⁻¹ Δy / Δx

         θ = tan⁻¹ (-13.85 + 22.52) / (-8 - 13)

         θ = tan⁻¹ (-8.67 / 21)

         θ = -22.4°

The negative sign indicates that the angle is measured from the axis clockwise.

In the form of cardinal s point is

     θ = 22.4 South of East