Question

Use appropriate units and signficant figures.

Answer 1

Answer:

D = 54.9 mi, 71.6 South of the East

Explanation:

In this exercise it is asked to find the displacement of the body, one of the easiest tasks is to dispose each displacement in a Cartesian coordinate system, let's use trigonometry

* first displacement d₁ = 67.0 mi

the angle is 35 south of east, measured from the axis x θ = -35

             cos -35 = x₁ / d₁

             sin -35 = y₁ / d₁

            x₁ = d₁ cos (-35)

            y₁ = d₁ sin (-35)

            x₁ = 67 cos 35 = 54.88 mi

            y₁ = -67 sin 35 = -38.43 mi

* second displacement d₂ = 40, mi

the angle is 20 to the west of the south, so mean from the axis x is

           θ = 180+ 20 = 200º

           cos 200 = x₂ / d₂

           sin 200 = y₂ / d₂

           x₂ = d₂ cos 200

           y₂ = d₂ sin 200

           x₂ = 40.0 cos 200 = -37.59 mi

           y₂ = 40.0 sin 200 = -13.68 mi

now we can find the displacement in each exercise

            X_total = x₁ + x₂

            X_total = 54.88 -37.59

            X_total = 17.29 mi

            Y_total = y₁ + y₂

            Y_total = -38.43 -13.68

             Y_total = - 52.11 mi

Let's use the Pythagorean theorem to find the displacement

             D = $\sqrt{x_{total}^2 + y_{total}^2}$

             D = $\sqrt { 17.29^2 + 52.11^2}$

             D = 54.9 mi

to find the angle let's use trigonometry

             tan θ = $\frac{y_{total} }{x_{total} }$

             θ = tan⁺¹ \frac{y_{total} }{x_{total} }

             θ = tan⁻¹ (-52.11 / 17.29)

             θ = -71.6º

the negative sign indicates that it is measured clockwise from the x-axis.

In cardinal coordinates it is 71.6 South of the East