Will These Two Planes Collide?

[Femme_physics]

Plane B flies in a direct line at constant velocity Vb = 848 km/h. Above him, at a distance of 7.5 km/h flies airplane A. Airplane A flies at a constant velocity Va = 2050 km/h. It flies in a vertical pathway in an arch of the radius R equal 5 km.

In the drawing is described the initial position of both planes.

If both planes carry on flying as described in the question, will they collide?

http://img687.imageshack.us/img687/5315/planthingy.jpg


Solution Attempt
I don't get how it's possible for them to collide. One just flies in an arch, so I guess that means in a circular pathway, that means that plane A will be directly at point B while plane B will be waaaaaaaay off ahead

Like this:

Right?

Or am I misreading/mistranslating something?

http://img803.imageshack.us/img803/8307/ababababa.jpg

 

[Doc Al]

Right?

Or am I misreading/mistranslating something?

You are misreading something. In your second diagram, the paths do not even overlap. But in the first diagram, you can see that the horizontal path of plane B will intersect the semi-circle path of plane A. (The question is at what time will the paths overlap.)

 

[Femme_physics]

No the question is "will they collide", not "at what time will they collide"

 

[phinds]

Just at a guess I'd say they will either collide or come quite close. You don't seem to understand the diagram. Plane B files slowly for a short distance and plane A flies a longer distance but at a higher speed and they meet up (or come close) at the point where their flight paths intersect, as clearly shown on the diagram (not on your diagram of course, which just illustrates your misunderstanding of the original diagram)

 

[Doc Al]

No the question is "will they collide", not "at what time will they collide"

Your incorrect interpretation: Since the paths don't even intersect, how can they possibly collide?

Correct interpretation: Ah... the paths do intersect. Figure out at what time they overlap to see if the planes collide.

 

[Femme_physics]

Is this the correct diagram, then?

http://img29.imageshack.us/img29/1249/correctinterp.jpg

 

[phinds]

yes, although you should do the math to see whether it's kaboom or just WHOA that was a near miss.

 

[Femme_physics]

yes, although you should do the math to see whether it's kaboom or just WHOA that was a near miss.

LOL great comment. Will do

 

[Femme_physics]

Well, I can start by finding the angular velocity of Va.

http://img560.imageshack.us/img560/259/vaabb.jpg

Now I have these formulas to relate angular velocity to distance:[URL]http://2.bp.blogspot.com/-MtFCi-xpX3M/TeXlOL9z7WI/AAAAAAAAAPI/pg9p6fiNFo4/s400/nusha.jpg[/URL]

But which angle do I use-- alpha or beta?http://img26.imageshack.us/img26/3026/alphaorbeta.jpg

And...am I at the right track?

 

[I like Serena]

Now I have these formulas to relate angular velocity to distance:

Try the third on the left, with angular acceleration equal to zero.
(Careful here: the alpha in your formula table is angular acceleration, which is not your angle alpha.)

But which angle do I use-- alpha or beta?

Try (beta + 90^o).

And...am I at the right track?

Yep.

 

[Femme_physics]

Glad to see you everywhere! :)

I don't understand how to use this formula you suggested-- I mean, do I just plug in the value in degrees?

i.e.

120 = 0.114t

?

 

[I like Serena]

Glad to see you everywhere! :)

I don't understand how to use this formula you suggested-- I mean, do I just plug in the value in degrees?

i.e.

120 = 0.114t

?

Same thing! :)

Usually we do everything in math and physics (all angles) in "radians".
Degrees is another unit for the same thing, so you have to convert.

180 degrees corresponds to $\pi$ radians.

Btw, you're not so much on the right track, but on the right trajectory!

 

[Femme_physics]

Ah, thanks,

Solved it! :D

http://img62.imageshack.us/img62/1008/pipipiw.jpg

Since the distance difference between them is so small, I guess that means KABOOMAGA!

Btw, you're not so much on the right track, but on the right trajectory!

LOL brilliant!

 

[I like Serena]

LOL brilliant!

Sorry, I take that back. You're on a bad trajectory, just because: KABOOMAGA!

 

[Femme_physics]

heh ;)

Shouldn't I use centripetal acceleration in this formula?

Or does it really stand for tangential acceleration?

http://img38.imageshack.us/img38/7299/ceentr.jpg

 

[I like Serena]

heh ;)

Shouldn't I use centripetal acceleration in this formula?

Or does it really stand for tangential acceleration?

Edited: It really stands for angular acceleration, which is similar to tangential acceleration.
(Tangential acceleration is not the same as angular acceleration - they differ by a factor R.)

Centripetal acceleration is quite another friend (which is radial).

 

[Femme_physics]

I'm trying to find the difference in aerial position after 10 seconds.

I found out through this formula

delta alpha = omega x time +at^2/2

That delta alpha - 1.13889

Converting that to degrees that 65.25 degrees

Now I'm not sure where is that angle. Is it here?http://img135.imageshack.us/img135/149/angleangle.jpg

 

[I like Serena]

Good morning Femme_physics!

Angles are used in circular motion.
An angle is measured between the line from the center of the circle to the initial position, up to the line between the center of the circle and the final position.

So no, it is not where you have drawn it.Edit: Oh, and please avoid using alpha in this context, because you're using a formula that uses alpha (not "a") for angular acceleration, which is zero is this problem (and will be in most problems that are coming your way).

 

[ehild]

Plane B flies in a direct line at constant velocity Vb = 848 km/h. Above him, at a distance of 7.5 km/h flies airplane A. Airplane A flies at a constant velocity Va = 2050 km/h. It flies in a vertical pathway in an arch of the radius R equal 5 km.

Just a note: If A flies at constant velocity it moves along a straight line, not along a circle. Its speed can be constant, instead.

ehild

 

[Femme_physics]

Good morning ILS! :)

[quotes]An angle is measured between the line from the center of the circle to the initial position, up to the line between the center of the circle and the final position.
[/quote]

Ah, makes sense!

Edit: Oh, and please avoid using alpha in this context, because you're using a formula that uses alpha (not "a") for angular acceleration, that is zero is this problem (and most problems that are coming your way for now).

Check confirmed and affirmed :) Got it.Now they're asking me to find the distance in "aerial line" between the two planes after 10 seconds. Which distance do they want? This or that?

http://img109.imageshack.us/img109/6171/dissss.jpg

Uploaded with ImageShack.us

 

[I like Serena]

Now they're asking me to find the distance in "aerial line" between the two planes after 10 seconds. Which distance do they want? This or that?

That.

 

[Femme_physics]

LOL! Left or right one, I mean?

 

[I like Serena]

LOL! Left or right one, I mean?

Right!
(one I mean)

 

[Femme_physics]

(text deleted)

Ah, I think I'm on to something then! Give me a moment :)

 

[Femme_physics]

Solved.

5.3 km :)

Thanks!