an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E. The wind velocity is 30 kilometers per hour in the direction N30 degrees W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?

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02-06-2022
Mathematics

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an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E. The wind velocity is 30 kilometers per hour in the direction N30 degrees W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?

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okpalawalter8 okpalawalter8 · Answer 1 · 2022-06-15T21:24:58+02:00

For an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E, the ground speed of the plane and its direction is mathematically given as

Vg=556.10km/hr

[tex]\theta=52.99East[/tex]

What is the ground speed of the plane and its direction?

Generally, the equation for the velocity of the plane is mathematically given as

[tex]Vp=Fcos\thetai+Fsin\theta j[/tex]

Therefore

Vp=530cos45i+530sin45j

Vp= 374.76i+374.76j

For wind speed

Vm=80cos(90+30)i+80sin(90+30)j

Vm=-40i+69.28j

Hence, there resultant is

Vr=Vm +Vp

Vr=374.76i+374.76j + 40i+69.28j

Vr=334.77i+1444.05j

In conclusion, the Ground speed is

[tex]Vg=\sqrt{334.77^2+1444.05^2}[/tex]

Vg=556.10km/hr

Direction

[tex]Tan \theta=\frac{444.05}{334.77}[/tex]

[tex]\theta=52.99East[/tex]