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...

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