Asked by music123
                The pilot of an airplane that flies with an airspeed of 800 km/h wishes to travel to a city 800 km due east. There is a 80 km/h wind FROM the northeast
a) what should the plane's heading be?
b) How long will the trip take?
            
        a) what should the plane's heading be?
b) How long will the trip take?
Answers
                    Answered by
            Damon
            
    A is angle he heads North of East
plane velocity due to wind in East direction = -80 cos 45
plane velocity due to heading in East dir = 800 cos A
total East component = 800 cos A - 80 cos 45
plane velocity due to wind in North direction = -80 sin 45
plane velocity due to heading in North dir = 800 sin A
We want ZERO North resultant so
800 sin A = 80 sin 45
sin A = 0.1 (.707) = 0.0707
A = 4 degrees North of East or 90 - 4 = 86 deg compass heading
now velocity component East = 800 cos 4 - 80 cos 45
= 798 - 56.56 = 741 km/hr East
800 / 741 = hours taken
    
plane velocity due to wind in East direction = -80 cos 45
plane velocity due to heading in East dir = 800 cos A
total East component = 800 cos A - 80 cos 45
plane velocity due to wind in North direction = -80 sin 45
plane velocity due to heading in North dir = 800 sin A
We want ZERO North resultant so
800 sin A = 80 sin 45
sin A = 0.1 (.707) = 0.0707
A = 4 degrees North of East or 90 - 4 = 86 deg compass heading
now velocity component East = 800 cos 4 - 80 cos 45
= 798 - 56.56 = 741 km/hr East
800 / 741 = hours taken
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