# Ground speed of a plane - vectors

1. Feb 17, 2009

### tinkus

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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

2. Feb 17, 2009

### HallsofIvy

Re: vectors

How do you get the "70j" here?

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. Feb 17, 2009

### tinkus

Re: vectors

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. Feb 17, 2009

### HallsofIvy

Re: vectors

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).

5. Feb 17, 2009

### tinkus

Re: vectors

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

6. Feb 17, 2009

### Staff: Mentor

Re: vectors

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.

7. Feb 17, 2009

### tinkus

Re: vectors

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