# Thread: Global minimum if plane A is flying 950km/h and plane is flying 850km/h

1. ## Global minimum if plane A is flying 950km/h and plane is flying 850km/h

Hello, I would need some help with this please:

Airplane A and airplane B move along vertical paths. At some point, from the penetration of their pathways, airplane A is 2300 km away and aircraft B 2000 km.
Specify the minimum distance of both airplanes if the airplane A is flying 950km/h and the airplane is flying 850km/h.

So, I get that plane A is at A[0,-2300] and plane B is at B[-2000,0] at some point.

I know how to find global minimum but I don't know how to make the quadratic equation from these parameters.

2. Originally Posted by martinekk
Airplane A and airplane B move along vertical paths.
Huh? How can planes fly "vertically"?

3. Couple of things:

1) "Penetration of their pathways" - Is that a point of intersection? If it is, then the minimum distance is 0 km. If it isn't, then this is difficult to interpret. Better translation?

2) If they are both on vertical paths, and you have them both at y = 0, the minimum distance is constant at 300 km.

3) If, as you actually have them, x = 0 and A is chasing B, eventually the distance will be zero. Obviously, that is the minimum distance.

Can you provide the EXACT text of the problem (maybe an accompanying drawing) and show YOUR best work? That would be very beneficial.

Note: I assumed "vertical" flight meant the positive y-direction from a bird's-eye view.

Uh, sorry for my bad english.

yeah i mean point of intersection

imagine that plane A is copying axis Y and plane B is copying axis X

at some point from intersection plane A is 2300 km before intersection and plane B is 2000km before it.

but planes have different speed (A=950km/h, B=850km/h)

from my calculations B will be there faster (2000/850 is lower than 2300/950)

I know that smallest distance between A and B is about 43.15km but I need the
equation to calculate it step by step.

Thanks for reply and hope you get me now.

5. I think you mean something like this:
Originally Posted by martinekk
imagine that plane A is following axis Y and plane B is following axis X.

At some
time plane A is 2300 km before intersection and plane B is 2000km before it,
but planes have different speed (A=950km/h, B=850km/h)

From my calculations B will be there faster (2000/850 is lower than 2300/950)

I know that smallest distance between A and B is about 43.15km but I need the
equation to calculate it step by step.
I would use the Pythagorean Theorem (distance formula) to express the SQUARE of the distance between the planes at time t, and try to minimize that. It will be a quadratic equation in t.

If you need more help, please show whatever work you have done, so we can guide you further.

6. Yeah, thank you.

I need to know how to make the square equation from parameters 2000, 2300, 950 and 850 to calculate minimum. Thank you.

7. You need an equation that represents the location. The speed is constant. The equation will be linear. Let's see what you get.

8. To use the distance formula, you need expressions in terms of time (t) for the x-coordinate of plane B and the y-coordinate of plane A.

Here's a hint: Let time be measured in seconds. A bug crawls along the x-axis (from right to left). The bug starts at (16,0) and travels 0.35cm each second. An expression for the bug's x-coordinate in terms of t is:

16 - 0.35 t

9. Yeah I think that's enough. Thank you very much.

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