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jet is flying at 500 mph east relative to the ground. A Cessna is flying at 150 mph 60° north of west relative to the ground. What is the Cessna's speed relative to the 747? A 634 mph B 578 mph C 590 mph D 444 mph E 610 mph

Respuesta :

Answer:

C. 590 mph

[tex]\vert v_{cj}\vert=589.49\ mph[/tex]

Explanation:

Given:

  • velocity of jet, [tex]v_j=500\ mph[/tex]
  • direction of velocity of jet, east relative to the ground
  • velocity of Cessna, [tex]v_c=150\ mph[/tex]
  • direction of velocity of Cessna, 60° north of west

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.

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