A pilot in an airplane with an airspeed of 100 km/h wishes to fly to a city 2000 km due east.  There is a wind blowing from 25 degrees at 100 km/h.In what heading should the pilot steer and what...

A pilot in an airplane with an airspeed of 100 km/h wishes to fly to a city 2000 km due east.  There is a wind blowing from 25 degrees at 100 km/h.

In what heading should the pilot steer and what will be the groundspeed of the airplane

Asked on by rosemin

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The pilot is travelling at an airspeed of 100 km/h towards the East. The pilot has to steer the airplane to tackle the wind which is blowing.

The wind is blowing at 100 km/h at an angle of 25 degrees to the west- east axis.

The velocity of the wind can be divided into its components towards the east and the north. The component to the north is 100* sin 25 and the component towards the east is 100*cos 25.

The pilot has to steer the plane so that the component of the wind towards the north of 100*sin 25 is cancelled. He steers his plane at an angle of -25 degrees at 100 km/h with respect to the west- east axis.

The velocity of the airplane now has two components, one towards the south equal to 100*sin 25 and one towards the East equal to 100*cos 25

The component of the velocity of the wind towards the north is cancelled by the component of the plane's velocity towards the south. The plane's net velocity is equal to 2*100*cos 25 = 200*cos 25.

The pilot has to steer in a direction making an angle of -25 degrees with the axis from the west to the east. The ground speed of the airplane is 200*cos 25.

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