SOLUTION: an airplane has an airspeed of 500 kilometers per hour in a northerly direction. the wind is 60 kilometers per hour in a south easterly direction. Find the actual speed and dirceti

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Question 30695: an airplane has an airspeed of 500 kilometers per hour in a northerly direction. the wind is 60 kilometers per hour in a south easterly direction. Find the actual speed and dircetion of the plane relative to the ground.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
I am hoping that south easterly means SSE --> South south east which means that it has a bearing of 45 degrees.
North to east is 90 degress so 90+45=135degrees
In vector form this forms a oblique triangle:


N

|500km/h

|

|135 degrees 

 \

  \

   \60km/h

    \

This allows us to use the cosine law:

Letting the unknow be in vector form of ||v+w||

Form cosine law: 





||v+w||≈ 544

TO find direction use sine law:









x ≈ 66





Hence, the ground speed of the plane is 544km/h making a direction of 66 degrees.

Paul.