How Do You Calculate the Speed of a Plane with Respect to the Ground?

[aruji73]

You are traveling on an airplane. The velocity of the plane with respect to the air is 120.0 m/s due east. The velocity of the air with respect to the ground is 43.0 m/s at an angle of 30° west of due north.

1.What is the speed of the plane with respect to the ground?

I got 82.76 by doing 120-43(cos30)

but apparently it was wrong the feedback i got was It looks like you incorrectly calculated the planes velocity with respect to the ground in the east direction. Be careful when you calculate the east-west component of the wind's velocity. Also don't forget to include the winds north-south component to get the total speed of the plane with respect to the ground.

 

[Simon Bridge]

Very good - did you have a question?

 

[aruji73]

ya that's apparently wrong how do I get the correct solution

 

[Simon Bridge]

Well, your answer does not have a direction or any units and you did not supply any reasoning.

The advise you have is that you made a mistake in your reasoning.
Go back over it again and consider - what does the wind do with the plane?
Perhaps if you drew a picture
- which direction is the "43cos(30)" part pointing in?
- which direction is the "120" part pointing in