Physics: Relative And Circular Motion

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You are on an airplane traveling 30° south of due west at 160 m/s with respect to the air. The air is moving with a speed 41 m/s with respect to the ground due north.

1.How far west will the plane travel in 1 hour?

Sep 10th, 2015

Thank you for the opportunity to help you with your question! I shall do my best to help you out!

The air is moving with a speed 30 m/s with respect to the ground due north 
Airplane is moving with a speed 160 m/s with respect to air due west. 

We have to first find the speed of Airplane with respect to the ground. 
Since the wind is having a speed of 30 m/s , it will move the air plane toward North as for as the earth is concerned . 
Hence we add the speed with the plane’s speed and find the resultant ot these two speeds. 
Since they are perpendicular to each other, the resultant is 

√ (160 ^2 + 30^2) = 162.79 m/s and the direction is given by tan θ = western velocity / northern velocity so that θ is the angle measured from North to west. 
tan θ = 30 / 160 and θ = 10.6° west of north . 

Therefore the speed of airplane is 162.79 m/s at angle 10.6° west of north viewed from the ground. 

Distance moved in one hour = 160*60*60 =576, 000 m. Therefore in one hour, the airplane would have traveled 576, 000 meters. 

I hope this helps! 

Please let me know if you need any clarification. I'm always happy to answer your questions. If you found my answer helpful, please take a moment to rate my portfolio. Thank you very much!
Sep 10th, 2015

Actually speed of 41 

Sep 14th, 2015

I sincerely apologize for that error. The answer would change to 165.2 m/s (instead of 162.79 previously calculated). 

If you need any help, please let me know. Thank you again for your cooperation! 

Sep 17th, 2015

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