Answer:
C. 590 mph
[tex]\vert v_{cj}\vert=589.49\ mph[/tex]
Explanation:
Given:
Taking the x-axis alignment towards east and hence we have the velocity vector of the jet as reference.
Refer the attached schematic.
So,
[tex]\vec v_j=500\ \hat i\ mph[/tex]
&
[tex]\vec v_c=150\times (\cos120\ \hat i+\sin120\ \hat j)[/tex]
[tex]\vec v_c=-75\ \hat i+75\sqrt{3}\ \hat j\ mph[/tex]
Now the vector of relative velocity of Cessna with respect to jet:
[tex]\vec v_{cj}=\vec v_j-\vec v_c[/tex]
[tex]\vec v_{cj}=500\ \hat i-(-75\ \hat i+75\sqrt{3}\ \hat j )[/tex]
[tex]\vec v_{cj}=575\ \hat i-75\sqrt{3}\ \hat j\ mph[/tex]
Now the magnitude of this velocity:
[tex]\vert v_{cj}\vert=\sqrt{(575)^2+(75\sqrt{3} )^2}[/tex]
[tex]\vert v_{cj}\vert=589.49\ mph[/tex] is the relative velocity of Cessna with respect to the jet.
