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Aaron is flying a helicopter with an air-relative velocity of 12.5 m/s to the West. A constant wind is also blowing the helicopter towards the South at 4.55 m/s relative to the ground. What is the velocity vector of the helicopter relative to the ground? What is the speed and direction relative to the East? How long does it take to travel 1 km?

Respuesta :

Answer:

Explanation:

Given

Velocity of helicopter relative to air 12.5 m/s to west

In vector form

[tex]V_{ha}=-12.5\hat{i}[/tex]

where [tex]V_h[/tex]= velocity of helicopter relative to ground

Also the velocity of air

[tex]V_a=4.55\hat{j}[/tex]

[tex]V_{ha}=V_h-V_a[/tex]

[tex]V_h=V_{ha}+V_a[/tex]

[tex]V_h=-12.5\hat{i}+4.55\hat{j}[/tex]

Speed relative to east[tex]=\sqrt{12.5^2+4.55^2}[/tex]

=13.302

For Direction

[tex]tan\theta =\frac{4.55}{-12.5}[/tex]

[tex]180-\theta =20[/tex]

[tex]\theta =160^{\circ}[/tex] relative to east

For 1 km travel it takes

[tex]t=\frac{1000}{13.302}=75.17 s[/tex]

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