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Ground speed of a plane - vectors

  • Thread starter tinkus
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  • #1
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Homework Statement



A plane is heading due east and climbing at he rate of 80kph. if its speed is 480kph and there's a wind blowing 100kph to the northeast, wha is the groundspeed of the plane

Homework Equations





The Attempt at a Solution


w=100cos45+100sin45= 70i+70j
480= vxi+ 70j+80k
vxi= 468
Groundspeed= 468i+70i+70j=538i + 70j = 543kph

or


480= vxi+70j
vxi= 475
Groundspeed = 475i +70i+70j = 545i + 70j = 549kph
 

Answers and Replies

  • #2
HallsofIvy
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Homework Statement



A plane is heading due east and climbing at he rate of 80kph. if its speed is 480kph and there's a wind blowing 100kph to the northeast, wha is the groundspeed of the plane

Homework Equations





The Attempt at a Solution


w=100cos45+100sin45= 70i+70j
480= vxi+ 70j+80kk
How do you get the "70j" here?

vxi= 468
Groundspeed= 468i+70i+70j=538i + 70j = 543kph

or


480= vxi+70j
vxi= 475
Groundspeed = 475i +70i+70j = 545i + 70j = 549kph
Again, where did you get the "70 j" as part of the airplane's velocity? If the airplane is going "due east" shouldn't it be 0j?
 
  • #3
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yea i thought as much but isn't the y-component of the windspeed part of the airspeed? Can you show me how to solve this problem?
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
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955


No, the "airspeed" is the speed through the air and is separate from the wind speed. And you surely can't have thought you should include the j (north-south) component but not the i (north-south) component?

The velocity relative to the air is vx i+ 80 k and the airspeed is 480 so [itex]vx^2+ 80^2= 480^2[/itex]. Once you have found that, the velocity relative to the ground is (vx+ 70)i+ 70j (the k component is not relevant to moving relative to the ground).
 
  • #5
13
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ok thanks, i got 547.8kph. the answer key is 548.6, i guess is still correct...
 
  • #6
33,478
5,168


You lost some precision by the very rough rounding you did early on.
100 [itex]\sqrt{2}[/itex]/2 is closer to 71 than it is to 70.

You will always get more precise results if you refrain from rounding until your final result.
 
  • #7
13
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Thanks, it was a complete oversight...duly noted
 

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