A jet moving at 500.0 km/ h due is in a region where the wind is moving at 120.0 km/h in a direction 30.00° north of east. What is the speed of the aircraft relative to the ground?

Answer :

nandhini123

Answer:

The speed of the aircraft relative to the ground is 606.9 [tex]m/s^2[/tex]

Explanation:

x-y coordinate system:  

x is Positive due East direction. Similarly  y is Positive due North Direction.

Now let us Decompose each vector into x-y

500 km/h due east = (500, 0)

120 km/h at 30 degree north of east

= [tex](120 cos(30), 120 \times sin(30))[/tex]

= [tex](120 \times \frac{\sqrt{(3)}}{2}, 120 \times \frac{1}{ 2})[/tex]

= [tex](60 \times \sqrt(3), 60)[/tex]

Adding  the vectors.

=[tex](500, 0) + (60 \times \sqrt{3}, 60)[/tex]

=[tex](500 + 60 \times \sqrt(3), 60)[/tex]

=[tex](500 + 60 \times 1.73, 60)[/tex]

=[tex](500 +103.8, 60)[/tex]

= (603.8, 60)

Returning back to polar form

Magnitude = [tex]\sqrt{603.923^2 + 60^2} = 606.9[/tex]

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