Answer:
8.6 miles
Explanation:
In order to calculate the straight-line distance between the starting point and the ending point, we need to resolve each part of the displacement into two perpendicular directions, let's say horizontal (x) and vertical (y) directions.
In the first part, Erica moves for 5.2 miles 25∘ north of east. Resolving into the two directions:
[tex]d_{1x} = 5.2 cos 25^{\circ}=4.7 mi\\d_{1y} = 5.2 sin 25^{\circ} =2.2 mi[/tex]
In the second part, Erica moves 5.0 miles north, so the components are
[tex]d_{2x} = 0\\d_{2y} = 5.0 mi[/tex]
So the components of the net displacement are
[tex]d_x = d_{1x}+d_{2x}=4.7+0 = 4.7 mi\\d_y = d_{1y}+d_{2y} =2.2+5.0 = 7.2 mi[/tex]
And the magnitude of the net displacement is
[tex]d=\sqrt{d_x^2 +d_y^2}=\sqrt{4.7^2+7.2^2}=8.6 mi[/tex]
