Collision. How is it possible?

1. Jun 16, 2011

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 [Broken]

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 [Broken]

Last edited by a moderator: May 5, 2017
2. Jun 16, 2011

Staff: Mentor

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.)

3. Jun 16, 2011

Femme_physics

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

4. Jun 16, 2011

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)

5. Jun 16, 2011

Staff: Mentor

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.

6. Jun 16, 2011

Femme_physics

Last edited by a moderator: May 5, 2017
7. Jun 16, 2011

phinds

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

8. Jun 16, 2011

Femme_physics

LOL great comment. Will do

9. Jun 20, 2011

Femme_physics

Last edited by a moderator: May 5, 2017
10. Jun 20, 2011

I like Serena

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

Try (beta + 90o).

Yep.

11. Jun 20, 2011

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

?

12. Jun 20, 2011

I like Serena

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!

13. Jun 20, 2011

Femme_physics

Last edited by a moderator: May 5, 2017
14. Jun 20, 2011

I like Serena

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

15. Jun 20, 2011

Femme_physics

Last edited by a moderator: May 5, 2017
16. Jun 20, 2011

I like Serena

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).

Last edited: Jun 20, 2011
17. Jun 21, 2011

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 [Broken]

Last edited by a moderator: May 5, 2017
18. Jun 21, 2011

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).

Last edited: Jun 22, 2011
19. Jun 21, 2011

ehild

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

20. Jun 22, 2011

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!

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 [Broken]