Math Is Fun Forum

vector velocity

Guest

Just a curious question.

If a spaceship is traveling at 90% the speed of light on the X axis.  And it is also traveling 90% the speed of light on the Y axis.  What is its velocity?

binaryman

Guest

Re: Just a curious question.

I know time dilates at velocities like that and the theoretical limit for velocity is light speed.  But, and perhaps I was just looking at a popularist version of explaining how the formula for time dilation is achieved - BUT - the algebra only considered the spaceship moving in one direction.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Just a curious question.

BUT - the algebra only considered the spaceship moving in one direction.

That's because algebra is not used, calculus and differential equations are.  In fact, because of the theory of relativity, we can rotate the universe (or for the more sane mind, rotate the coordinate axes) till we are actually traveling in only one direction.  Remember, direction, along with everything else, is relative.

To make speed more meaningful, consider the distance after one second, time being relative to the traveler.  All other factors ignored, you will have traveled .9 lightseconds in both the x and y directions.  This corresponds to traveling 1.342 lightseconds in one second.  You are therefore traveling at 1.342 times the speed of light.

This of course is not possible.  Einstein's theory talks about 4 dimensional space time: (x, y, z, t).  It says that |x|+|y|+|z|+|t| = c, where c is the speed of light.  This actually shows why time dilates, but it is irrelevant to this problem so long as we take the location relative to the traveler (and thus, it is the universe that is moving so the universe has it's time dilated).  But the point is, that |x| + |y| certainly can't be greater than c, which were your conditions in the problem.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Just a curious question.

The fastest most spaceships can go is 1/1.4142136 the speed of light in each perpendicular right angle east and north, because then it is going the speed of light at a 45 angle, the maximum speed of most ships, they say.  So your problem is incorrect in the first place.
You are over the speed of light, not possible.  Unless it is a tesseract or something else.

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igloo myrtilles fourmis

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Just a curious question.

That isn't entirely correct, John.  It depends how you define speed.  As Hubble discovered, the universe is constantly expanding.  If we define speed in terms of distance and time while taking this into account, if two points are sufficiently distant from each other, the space in between will be expanding at such a rate that the two points will move away from each other at the speed of light.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

simransaxena

Member

Registered: 2008-10-10

Posts: 1

Re: Just a curious question.

Place the digits 1 to 9 in the space marked x below. use each digit once only.
how may solutions can u find?

       x x x
    -  x x x
     --------
      x x x

thanks
simran