Question

A pilot on a heading of 320^o with an air speed of 240 km/h. Her actual ground velocity is 250 km/h at a bearing of 318^o. Calculate the speed and direction of the wind.

Please include the equation we are trying to solve values for as I get confused easily! Thank you in advance.

Answer 1

All the data have been marked in the figure directly

The above data says that the angle of aeroplane shifts from 318o to 320o (by 2o ) when wind is occured.

denotes the wind velocity 'c' denotes the direction of wind ( THE DIRECTION OF SHIFT OF ANGLE)

We can find by cosine law,

Cosine law

For any triangle , the law of cosines states that any side can be written as

In this case

Now to find diection of wind

Using Sine Law of Triangle

It states that in a triangle( not right angleed one), the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

Here we take the sides 'a' and 'c'

if WE SHIFT THE VELOCITY DIRECTION UPWARS AND DRAW THE DIRECTIONS WE CAN SEE THAT

THE WIND VELOCITY IS 39.40o FROM NORTH TOWARD EAST = N39.4o E