Ground speed of a plane - vectors

[tinkus]

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

 

[HallsofIvy]

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?

 

[tinkus]

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?

 

[HallsofIvy]

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 vx^2+ 80^2= 480^2. 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).

 

[tinkus]

ok thanks, i got 547.8kph. the answer key is 548.6, i guess is still correct...

 

[Mark44]

You lost some precision by the very rough rounding you did early on.
100 \sqrt{2}/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.

 

[tinkus]

Thanks, it was a complete oversight...duly noted