A pilot in an airplane with an airspeed of 1000 km/h wishes to fly to a city 2000 km due east. There is a wind blowing from 25 degrees at a speed of 100 km/h.  In what heading should the pilot steer? and what will be the groundspeed of the airplane? I asked this question before but was given the wrong answer.  The answer at the back of my textbook says 84.8 degrees for the heading and 953.6 km/h for the groundspeed.  However, I don't know how to get these answers.  Please help! Thanks.

Expert Answers

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I assume the earlier answer did not match your solution as you had not specified the exact direction of the wind. It is blowing from 25 degrees, but 25 degrees to what. Also, you had specified the speed of the airplane as 100 km/hr instead of 1000 km/hr

From the results you have given, the direction of the wind is at an angle of 25 degrees to the north-south axis.

Now the pilot wants to fly the airplane along the west-east axis.

Let the heading of the pilot be an angle X made with the south-north axis.

We get the components of the wind as 100*sin 25 in the west direction and 100*cos 25 in the south direction.

The components of the airplane's velocity are 1000*sin X in the east direction and 1000*cos X in the north direction.

As the plane has to fly to the East, the component of the airplane's velocity toward the north has to cancel the component of the wind's velocity towards the south.

1000*cos X = 100*cos 25

=> cos X = 100*cos 25/ 1000

=> cos X = cos 25/ 10

=> X = arc cos( cos 25/10)

=> 84.8 degrees

The ground speed of the plane is the component of the airplane's velocity towards the East - component of the wind's velocity towards the West.

=> 1000* sin 84.8 - 100*sin 25

=> 953.62 km /h

The heading of the pilot should be 84.8 degrees made with the South-North axis and the ground speed is 953.62 km/h

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