Answer:
8.6 miles
Explanation:
We need to calculate the components of the total displacement along the east-west and north-south directions first.
In the first part, Erica moves 5.2 miles at 25∘ north of east. So the components of this displacement along the two directions are:
East: [tex]d_{1x} = 5.2 cos 25^{\circ}=4.7 mi[/tex]
North: [tex]d_{1y} = 5.2 sin 25^{\circ}=2.2 mi[/tex]
In the second part, Erica moves 5.0 miles north. So, the components of this displacement are:
East: [tex]d_{2x}=0[/tex]
North: [tex]d_{2y} = 5.0 mi[/tex]
So the components of the total displacement are
East: [tex]d_x = d_{1x}+d_{2x}=4.7 + 0 = 4.7 mi[/tex]
North: [tex]d_y = d_{1y}+d_{2y}= 2.2 + 5.0 = 7.2 mi[/tex]
Therefore the magnitude of the displacement, which is the straight-line distance from the starting point to the end of the race, is
[tex]d=\sqrt{d_x^2 +d_y^2}=\sqrt{4.7^2+7.2^2}=8.6 mi[/tex]
