The Jet is flying with an speed of 480 miles per hour at a bearing of .

Ground speed of the plane due to wind  is 518 miles per hour at a bearing of .

(a)

Draw the diagram for the situation:   

(b)

Find the speed and direction of the wind:

Observe the graph,

Air speed component is bearing at a means that it makes an angle of from the horizontal.

Similarly, Ground speed component is bearing at a means that it makes an angle of from the horizontal.

Component form of a vector is .

Ground speed component is the resultant of vector representing the air speed of the jet and the vector representing the wind.

Let the air speed component as .

Substitute and in the component form.

Let the resultant ground speed component as .

Substitute and in the component form.

Let the resultant wind speed component as .

Resultant ground speed component can be  written as,

.

Substitute and in above expression.

Magnitude of the wind speed:

.

Magnitude of the wind speed is 46.11 miles per hour.

Direction of the wind speed:

.

From the horizontal means plane is at a bearing .

Direction of the wind speed .

(c)

Pilot increased air speed of the plane to 500 miles per hour.

Component form of a vector is .

Substitute and in the component form.

Wind speed component .

Substitute and in .

.

Magnitude of the resultant ground speed:

Magnitude of the resultant ground speed is 538 miles per hour.

Direction of the ground speed:

.

From the horizontal means plane is at a bearing .

Direction of the plane is  .

(a)

(b)

Magnitude of the wind speed is 46.11 miles per hour.

Direction of the wind speed .

(c)

Magnitude of the resultant ground speed is 538 miles per hour.

Direction of the plane is  .