Vectors in the Plane: Plane+Wind question

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SUMMARY

The discussion centers on calculating the groundspeed and direction of an airplane with an airspeed of 430 mph at a bearing of S 45 degrees E, influenced by a wind speed of 35 mph from N 30 degrees E. The correct calculation involves vector addition, yielding a groundspeed of 440.3 mph, contradicting the textbook's stated value of 422.3 mph. The discrepancy highlights potential errors in the textbook, emphasizing the importance of verifying calculations in vector problems.

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Homework Statement


An airplane has an airspeed of 430 mph at a bearing of S 45 degrees E. If the wind is 35 MPH in direction of N 30 degrees E, find groundspeed and direction of plane.


Homework Equations


[[v]]([cos theta], [sin theta])


The Attempt at a Solution



430(cos 315,sin315)+35(cos30,sin30)=?<334.4,-286.6>
[[v]]=?~440..

Back of book says that the ground speed is 422.3.. and if i go the vector wrong, that means magnitude and direction will be wrong also.. Where did I go wrong?
 
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If the numbers you give are correct, then you have it right. The ground speed is 440.3, not 422.3.
 
Hope you're right. This isn't the 1st time the book has a typo or something.
 

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