# Math Help - Vector word problem

1. ## Vector word problem

"An airplane has an airspeed of 160 km/h. It is to make a flight in a direction of 75 degrees while there is a 25 KM/H wind from 345 degrees. What will the airplane's actual heading be?"

The example problem uses like 3 seperate sketches before getting to an answer, so I was wondering how people here would solve it.

Thanks guys! ( P.S., this is straight from the homework assignment, but I'll be clicking 'similar exercise' after following along with the steps you guys use and replicating getting to the right answer a few times. )

Edit: There is a new problem further on down of a similar type! Thanks!

2. Originally Posted by Wolvenmoon
"An airplane has an airspeed of 160 km/h. It is to make a flight in a direction of 75 degrees while there is a 25 KM/H wind from 345 degrees. What will the airplane's actual heading be?"

The example problem uses like 3 seperate sketches before getting to an answer, so I was wondering how people here would solve it.

Thanks guys! ( P.S., this is straight from the homework assignment, but I'll be clicking 'similar exercise' after following along with the steps you guys use and replicating getting to the right answer a few times. )
assuming that the directions are relative to true North ...

the wind direction is perpendicular to the intended airplane track, making the air vector the hypotenuse of the right triangle formed by the air, wind, and ground vectors.

the crab angle (angle that the aircraft turns into the wind) is

$\theta = \arcsin\left(\frac{25}{160}\right) \approx 9^\circ$

so the aircraft heading is $066^\circ$ , and the ground speed is $\sqrt{160^2 - 25^2} \approx 158$ km/hr

3. Almost have that, can you show it graphically? *Is working on it*

4. Okay...second, follow up problem ( will edit first post with this one too ):

"What bearing and airspeed are required for a plane to fly 400 miles due north in 2.5 hours if the wind is blowing from a direction of 347 degrees at 16 mph ) "

(all bearings are assumed due north

Okay, when sketching this I put 160 directly on the Y axis, then had it show me the example problem, which says to subtract 180 degrees from 347 to get angle C. Why am I doing this?

Then later on in the problem, after an application of the law of cosines to find side c is 176 MPH, I use the law of sines to get angle A, which is approximately 1 degree. I have no clue what to do with this answer so I go through the example and it tells me to subtract that from 360 to get 359 degrees. Why?

5. Originally Posted by Wolvenmoon
Okay...second, follow up problem ( will edit first post with this one too ):

"What bearing and airspeed are required for a plane to fly 400 miles due north in 2.5 hours if the wind is blowing from a direction of 347 degrees at 16 mph ) "

(all bearings are assumed due north

Okay, when sketching this I put 160 directly on the Y axis, then had it show me the example problem, which says to subtract 180 degrees from 347 to get angle C. Why am I doing this?

Then later on in the problem, after an application of the law of cosines to find side c is 176 MPH, I use the law of sines to get angle A, which is approximately 1 degree. I have no clue what to do with this answer so I go through the example and it tells me to subtract that from 360 to get 359 degrees. Why?
the airplane turns into the wind 1 degree to make good a track of 360 (due north) because the wind is coming from slightly left of due north ... one degree left of 360 is 359.

6. This got me on the practice final. I have a new problem, this text is ALL that is given to me for the problem, no charts, nothing.

"An airplane has an airspeed of 130 km/h. It is to make a flight in a direction of 70 degrees while there is a 20 km/h wind from 340 degrees. What will the airplane's actual heading be?"

Answer is 61 degrees. That is the exact problem given to me.

Argh, this is hard to explain! *Gets out MS paint*

Okay, so I'm a graphical learner/ I work best when I can see it drawn out when it deals with space and this is in the section about vectors, so seeing this put onto a parallelogram or sketched would make a huge difference to me.

The homework problem with the worked examples is still an enigma to me.