Navigating Wind: Flying East in a Light Airplane

[mybrohshi5]

Homework Statement

You are flying in a light airplane spotting traffic for a radio station. Your flight carries you due east above a highway. Landmarks below tell you that your speed is 52.0 m/s relative to the ground and your air speed indicator also reads 52.0 m/s. However, the nose of your airplane is pointed somewhat south of east and the station's weather person tells you that the wind is blowing with speed 19.0 m/s.

Homework Equations

N/A

The Attempt at a Solution

i tried drawing a diagram 52 being directly on the east line then another line going southwest from the end of the east line and that was my 19 then the resulting line was also a 52.

i found the angle between the two 52 lines to be 21.1 degrees but this is incorrect so i thought maybe it was 68.9 degrees since its the angle east of north but that is also wrong :(

any suggestions? any pictures would also be very helpful if possible.

thank you

 

[tiny-tim]

Hi mybrohshi5!

You haven't told us how the question asks for the answer to be written … is it just a heading (< 360º)? or is it a compass thing, like 20º south of east?

Anyway, yes, your diagram is correct, but I don't quite make it 21.1º …

what formula did you use?

 

[mybrohshi5]

Sorry i thought i had it in there.

It wants What direction is the wind blowing (in degrees east of north)

I used the law of cosines to come up with the angles i got but neither of the answers are correct.

 

[tiny-tim]

Sorry i thought i had it in there.

It wants What direction is the wind blowing (in degrees east of north)

I used the law of cosines to come up with the angles i got but neither of the answers are correct.

Hi mybrohshi5!

ah, "East of North" would be 90º plus that angle (because East is 90º East of North ).

(and yes, the law of cosines is fine, but in this case since two sides are the same, I'd have saved time by using tan^-1 9.5/52, and then doubling it )

 

[mybrohshi5]

i just tried the answer 111 and that is incorrect. i did the tan^-1(9.5/52) = 20.7 + 90 = 110.7 so i rounded to 111 cause I am sure it only wants 3 sig figs like always cause its mastering physics but it said it was wrong?

any suggestions? thank you

 

[tiny-tim]

D'oh!

I've been making the same mistake as you, I've been finding the heading of the airplane.

(i thought that was the question originally, and i didn't notice when it was changed )

The heading of the wind is 90º minus the other angle of the triangle.

 

[mybrohshi5]

it is also not 69.3 (90-20.7) or 79.7 (90-10.35) :( i have one try left and would like to get it right.

any other suggestions?

 

[mybrohshi5]

so is the answer 100.35?

90+10.35 = 100.3533

 

[tiny-tim]

so is the answer 100.35?

90+10.35 = 100.3533

Slow down …

The top-left angle of the triangle is (roughly) 2 x 10º.

So the top-right angle is (roughly) 80º.

So the wind is (roughly) 80º North of East.

So that's … East of North?

 

[mybrohshi5]

80 degrees north of east would be 20 degrees east of north correct? i tried that though. well i tried 21.1 degrees east of north and that was wrong?

 

[tiny-tim]

80 degrees north of east would be 20 degrees east of north correct?

Noooo …

10º ​

 

[mybrohshi5]

haha 10.35 was correct. i can't even subtract right anymore. this problem killed me LOL.

Thanks for all your help