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
- [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]
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