What Flaw Exists in Calculating Speed When Accelerating in Two Dimensions?

[tedcan]

Ok a lot of people smarter than me have probable thought of this and know the flaw in my logic. However working in a guard tower in Iraq... I can't find the flaw only that I know it must be there. here is the question?
I accelatea spaceship along the x-axis to 0.9 x the speed of light. then I accelarte it allong the y-axis to 0.9 x the speed of light. now relitive to the x-axis the ship is only travling 0.9 x the speed of light same with relitive to the y-axis however along the 45 degree it is travleing aprox 1.2 times the speed of light which is impossible so where is the flaw in my logic... Thanks from a soldier who loves physics

 

[theCandyman]

I think that is a good question. I had asked my high school teacher a question along the same lines when we were told that no two objects could travel the speed of light relative to each other. My question went, would not a metorite traveling 99 percent the speed of light past another metorite going 99 percent the speed of light in the opposite direction be going over the speed of light past each other?

In truth, there is an equation to calculate that, which I looked up (from it I guessed that the numerical answer to my question was something along 99.999999 percent the speed of light). I have forgotten it, sorry.

 

[tedcan]

Thanks, but if possible can someone show me the math or a website or keyword I can use to look it up. my mind is really craving order on this problem. Thanks again

 

[fasterthanjoao]

i'll draw a simple diagram.

------------------- (motion along x-axis)

|
| (motion along y-axis)
|

|
| (the way you're thinking about the problem...)
-------------------|

However, mathematicians ignore - the spaceship is actually traveling diagonally, if you think about it - when the ship is moving along the x-axis, and you start accelerating along y, the motion along the x still exists, and although you can consider motion in both axes as components, they don't represent the true velocity.

and well, by einsteins relativity the object will eventually struggle greatly in its acceleration, until it can't possibly go any faster. [always <c]

i don't know how good your maths is, but if you're still interested in this sort of stuff, have a browse on Lorentz-Transformations which show the 'correction' factors involved when it comes to near-speed of light travel.

 

[fasterthanjoao]

websites;

http://www2.slac.stanford.edu/vvc/theory/relativity.html

http://en.wikipedia.org/wiki/Lorentz_transformations (has some matrices and such)

http://www.phy.ntnu.edu.tw/java/relativity/relativity.html (amination example of relativity)


just incase that isn't enough..

http://scienceworld.wolfram.com/physics/SpecialRelativity.html

Nothing is really specific to your problem, it really just hinges on simple relativity principles and components of velocity.

 

[tedcan]

Thanks I understood the angluar velocity. why I asked the question but eh stuff on Lorentz-Transformations is exactly what I was looking for. give me something good to think about on the towers... perfect