The airspeed of an airplane is 600 km/hr, and there is a wind blowing northeast at 90 km/hr. if the airplane needs to head due north, at what angle does the pilot need to fly the plane?

The pilot has to fly the plane at an angle 83° north of west.

Explanation:

The airspeed of an airplane is 600 km/hr ( north direction)

In figure,

A wind blowing northeast at 90 km/h

In figure,  

Let actual speed of airplane and direction of plane,

Speed = x km/h

Direction = Ф (north of west, refer figure)

Now, we divide each velocity in horizontal and vertical component.

Horizontal component,

Vertical component,

Horizontal component,

Vertical component,

If the airplane needs to head due north.

Horizontal component must be cancel out.

Therefore,

Speed of airplane is 600 km/h due to north.

So, Sum of vertical component must be equal to 600

Therefore,

Using eq(1) and eq(2) we get,

Hence, The pilot has to fly the plane at an angle 83° north of west.

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