Vector Applications (Headings/Bearings)

[Sesto]

A pilot wishes to fly from point A to point B, a distance of 100 km on a bearing of 105°. The speed of the plane in still air is 240 km/h. A 20 km/h wind is blowing on a bearing of 210°. Remembering that she must fly on a bearing of 105° relative to the ground (ie the resultant must be on that bearing), find

a) the heading she should take to reach her destination
b) how long will the trip take

I know how to find B, as I just need to take the distance divided by the velocity of the resultant vector. My only problem is finding the heading what she should take. Can someone help explain how I start this question? A diagram would be nice (more of a visual learner) but it isn't needed.

[Deleted]

Are people doing your homework for you? This is the second one today.

[Blueobelisk]

Once again, the smartest man on this forum stands in front of you.

But I don't feel like drawing. Lets just do this analytically as opposed to drawing everything.

Just break stuff up into their components, including their angles in the terms (you may have to draw small triangles).

[Sesto]

Are people doing your homework for you? This is the second one today.

There is a difference between 'doing' and 'helping'. I'm not asking them to do the question, I'm asking them to help me understand how to do the question.

Once again, the smartest man on this forum stands in front of you.

But I don't feel like drawing. Lets just do this analytically as opposed to drawing everything.

Just break stuff up into their components, including their angles in the terms (you may have to draw small triangles).

I understand this. I can break down the wind vector into components easily, but I obviously can't do that for the plane vector because I don't have the heading for it. I don't understand how to get the heading either, hence the point of this thread.

[Blueobelisk]

They're just asking you to find which way the plane should fly. There are three total vectors here:
-The way the plane pilot steers.
-The way the wind blows
-The way the plane travels as a result of the wind blowing and the pilot steering.

They tell you that you have to travel 100 KM in a 105 degree direction. You have which direction and speed the wind is blowing. You have how fast the plane can travel. You just need to know which angle the plane pilot needs to steer.

[Sesto]

They're just asking you to find which way the plane should fly. There are three total vectors here:
-The way the plane pilot steers.
-The way the wind blows
-The way the plane travels as a result of the wind blowing and the pilot steering.

They tell you that you have to travel 100 KM in a 105 degree direction. You have which direction and speed the wind is blowing. You have how fast the plane can travel. You just need to know which angle the plane pilot needs to steer.

I know... but I don't know how to get the angle the plane pilot needs to steer. I don't understand how breaking the vectors into components can be done. I can do that for the wind vector, but I can't do it for the plane vector or the resultant vector. The plane vector I am missing the angle the plane pilot needs to steer (hence the question), and I obviously can't get the resultant vector yet, as I don't have the magnitude.

If I could figure out the resultant vector I could find the angle the pilot needs to fly. I'm guessing I need to somehow find it considering they gave me the final bearing, but I don't know how I can use the final bearing to find the components of the resultant without the magnitude.

[Blueobelisk]

Gonna play Saints Row 4. Find the question mark.

[Psynyx]

calculating plan direction vector relative to wind velocity -- Well someone drew it for you, but if you had searched google you would have been able to find how to answer this question pretty easily.

[Tirivaria]

I know... but I don't know how to get the angle the plane pilot needs to steer. I don't understand how breaking the vectors into components can be done. I can do that for the wind vector, but I can't do it for the plane vector or the resultant vector. The plane vector I am missing the angle the plane pilot needs to steer (hence the question), and I obviously can't get the resultant vector yet.

You have the magnitude of the plane vector. Consider that to be the hypotenuse of a right triangle. Therefore the x and y legs of the triangle are 240 sin theta and 240 cos theta. You can get the x and y components of the wind vector and what you want your resultant vector to be. Stick them in equations and solve for theta.

Edit: Blueobelisk's picture is better.

[Crianthia]

God how I don't miss physics HW. Are you able to get it yet or still need help?

[poser765]

[Sesto]

You have the magnitude of the plane vector. Consider that to be the hypotenuse of a right triangle. Therefore the x and y legs of the triangle are 240 sin theta and 240 cos theta. You can get the x and y components of the wind vector and what you want your resultant vector to be. Stick them in equations and solve for theta.

Edit: Blueobelisk's picture is better.

I now understand this, but I fail to see how I can get what I want my resultant vector to be. Plus I don't think (granted, I'm probably wrong) that the picture is correct. Wouldn't that be if it was drawn to the y axis? Aren't you supposed to draw the right triangle to the x axis? In that case, for the angle you'd use for the wind vector would be 60, not 30, and the resultant vector would have been 15, not 75. Considering I don't understand the question in the first place I'm guessing I'm wrong, I just want to make sure.

If the Wind Vector was

Vw = [-20cos60, -20sin60]
= [-10, -17.32]
and the plane vector was

Vp = [240costheta, 240sintheta]

and the resultant vector was (x being the magnitude of the resultant vector)

Vr = [xcos15, xsin15]

Conisdering

Vw + Vp = Vr
[-20cos60, -20sin60] + [240costheta, 240sintheta] = [xcos15, xsin15]

I have two missing numbers. Theta and the magnitude of the resultant. Considering the whole point of the question requires finding theta, I must be able to find the magnitude of the resultant somehow... how?



Also really sorry about this guys, I'm sure I'm just dense and missing something incredibly obvious. I just really need to figure out how to do this question.

[Tirivaria]

I'm have two missing numbers. Theta and the magnitude of the resultant. Considering the whole point of the question requires finding theta, I must be able to find the magnitude of the resultant somehow... how?

You have 2 equations (x-axis and y-axis) and 2 unknowns. Just solve the system of equations.

Once you have the magnitude of the resultant, you're halfway to answering part b.

[Sesto]

You have 2 equations (x-axis and y-axis) and 2 unknowns. Just solve the system of equations.

Once you have the magnitude of the resultant, you're halfway to answering part b.

If my numbers are correct (are they?) then that means the two equations are (theta being y)

-20cos60 + 240cosy = xcos15
-20sin60 + 240siny = xsin15

So I just solve the system of equations? It looks to be a really complicated process... I just want to make sure I'm understanding this correctly before I attempt it...

[Tirivaria]

If my numbers are correct (are they?) then that means the two equations are (theta being y)

-20cos60 + 240cosy = xcos15
-20sin60 + 240siny = xsin15

So I just solve the system of equations? It looks to be a really complicated process... I just want to make sure I'm understanding this correctly before I attempt it...

I didn't look closely at your numbers. Just to see if you had the concept. Just remember that the problem is giving you "bearings" which are angles from an absolute point of reference while you're computing using angles relative to the triangles you drew for each vector.

Just draw a picture (maybe a bit more to scale than blueobelisks's) and make sure if those should be + or - in your equations.

[Sesto]

I didn't look closely at your numbers. Just to see if you had the concept. Just remember that the problem is giving you "bearings" which are angles from an absolute point of reference while you're computing using angles relative to the triangles you drew for each vector.

Just draw a picture (maybe a bit more to scale than blueobelisks's) and make sure if those should be + or - in your equations.

Okay I drew the wind vector and the resultant vector.

Wind Vector
Resultant Vector

I need to know if my 30 degrees and 15 degrees for the wind and resultant vectors are correct. I understand how blue obelisk got his numbers, he just drew the triangles using the y axis as his base, but I'm pretty sure that's wrong. If someone could tell me if I'm right or wrong with how I drew the triangles, I could actually use the numbers and begin solving the system of the equations.

[Asics]

Sorry to go off topic, but damn. Maybe being a pilot isn't in the books for me =(

[Sesto]

Sorry to go off topic, but damn. Maybe being a pilot isn't in the books for me =(

I'm pretty sure you won't ever have to use vectors to determine what course you need to take, as you'd be given that information or the computer would calculate it for you. So I think you should be okay...

[poser765]

I'm pretty sure you won't ever have to use vectors to determine what course you need to take, as you'd be given that information or the computer would calculate it for you. So I think you should be okay...

You do, sort of. Some forms of navigation use some trig to do exactly what is asked in the OP. The reality is there are tools to do it for you. See the E6B I posted above. Also that form of navigation, called dead reckoning isn't nearly as prevalent as using GPS or land based radio aids for navigation. A further reality is the extant of math I use as a professional pilot is simple arithmetic. lol mainly subtracting days worked from days scheduled to work so I know when the fuck I get to go home for a couple of days.

[Sesto]

Okay... I was just told by my teacher that I should be doing this by using sinelaw, not by finding the components (for the first part of the question). I don't need to use a system of equations.