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 27.0 m in a direction 60.0 ∘ west of north. Jane walks 12.0 m in a direction 30.0 ∘ south of west. They then stop and turn to face each other.In what direction should Ricardo walk to go directly toward Jane?

Answer 1

Answer:

The direction Ricardo walk to go directly toward Jane is 31.13°.

Explanation:

Given that,

Ricardo walks 27.0 m in a direction 60.0 ∘ west of north.

Jane walks 12.0 m in a direction 30.0 ∘ south of west.

We need to calculate the separation distance between  them

Using cosine rule

$d=\sqrt{(h)^2+(l)^2-2\times h\times l\cos\theta}$

Put the value into the formula

$d=\sqrt{(27)^2+(12)^2-2\times27\times12\cos60}$

$d=23.43\ m$

We need to calculate the direction should Ricardo walk to go directly toward Jane

Using formula for direction

$\dfrac{d}{\sin\theta}=\dfrac{l}{\sin\theta}$

Put the value into the formula

$\dfrac{23.43}{\sin60}=\dfrac{12}{\sin\theta}$

$\sin\theta=\dfrac{12\times\sin60}{23.43}$

$\theta=\sin^{-1}(0.443)$

$\theta=26.29^{\circ}$

Hence, The direction Ricardo walk to go directly toward Jane is 26.29°.