Answer:
d = 447.21 km
θ = 26.6º the two distances are negative, this angle is in the third quadrant
Explanation:
This is a vector addition exercise, the easiest way to solve it is to add the vectors that have the same axis.
East-West (x-axis)
dₓ = 300 - 700
dₓ = - 400 km
the negative sign indicates that it is moving west
North-South (y axis)
[tex]d_{y}[/tex] = 400 -600
d_{y} = - 200 km
the negative sign indicates moving towards the South
now we can use the Pythagorean theorem to find the modulus
d = √ (dₓ² + d_{y}²)
d = √ (400² + 200²)
d = 447.21 km
the direction of movement can be found with trigonometry
tan θ = d_{y} / dₓ
θ = tan⁻¹ (200/400)
θ = 26.6º
Since the two distances are negative, this angle is in the third quadrant
