Relavistic velocity lorentz transformation problem.

In summary, the problem involves two space ships approaching each other, with one moving at a speed of 0.9c relative to Earth. The task is to find the speed of one ship relative to the other, using the formula u'(x)=u(x)-v/(1-v*u(x)/c^2). By plugging in the values of u(x) and v, the speed of the second ship can be calculated in the first ship's frame of reference.
  • #1
Benzoate
422
0

Homework Statement


Two space ships are approaching each other

a)if the speed of each is .9 *c relative to Earth , what is the speed of one relative to the other

b)if the speed each relative to Earth is 30000m/s, what is the speed of one relative to the other


Homework Equations


The problem does not state if the two rockets are headed toward each other on the x-axis , y-axis or z-axis , so I'm not really sure what velocity equations I should used and so I will list them all.
u'(z)= u(z)/(gamma*(1-(v*u(z))/c^2)
u'(y)= u(y)/(gamma*(1-(v*u(x))/c^2)
u'(x)=u(x)-v/(1-v*u(x)/c^2)


/

The Attempt at a Solution



Here is my attempted solution for the first part part of the problem:
a) u'(z)=u(z)-.9c/(2.29*((1)- u(z)*(.9c)/c^2))
u'(y)= u(y)/(2.29*((1)-u(y)*(.9c)/c^2))
u'(x)=u(x)-.9c/(1-.9c*u(x)/c^2)

not sure how to calculate u(z),u(x), or u(y).
 
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  • #2
Benzoate said:

Homework Statement


Two space ships are approaching each other

a)if the speed of each is .9 *c relative to Earth , what is the speed of one relative to the other

b)if the speed each relative to Earth is 30000m/s, what is the speed of one relative to the other


Homework Equations


The problem does not state if the two rockets are headed toward each other on the x-axis , y-axis or z-axis , so I'm not really sure what velocity equations I should used and so I will list them all.
u'(z)= u(z)/(gamma*(1-(v*u(z))/c^2)
u'(y)= u(y)/(gamma*(1-(v*u(x))/c^2)
u'(x)=u(x)-v/(1-v*u(x)/c^2)


/

The Attempt at a Solution



Here is my attempted solution for the first part part of the problem:
a) u'(z)=u(z)-.9c/(2.29*((1)- u(z)*(.9c)/c^2))
u'(y)= u(y)/(2.29*((1)-u(y)*(.9c)/c^2))
u'(x)=u(x)-.9c/(1-.9c*u(x)/c^2)

not sure how to calculate u(z),u(x), or u(y).


You don't have to do all three! They are moving stratight toward one another, so both motions are along a comon straight line. You may call this line the x-axis and just do th ecalculation along x. "v" will be the speed of one of the spaceship as measured from Earth, u(x) will be the velocity of the second spaceship as seen from Earth and u'(x) will be the answer you are looking for.
 
  • #3
nrqed said:
You don't have to do all three! They are moving stratight toward one another, so both motions are along a comon straight line. You may call this line the x-axis and just do th ecalculation along x. "v" will be the speed of one of the spaceship as measured from Earth, u(x) will be the velocity of the second spaceship as seen from Earth and u'(x) will be the answer you are looking for.

so for one rocket ship , v=.9*c ,u(x)= u'(x) +v/((1+vu'(x)/c^2);

for the other rocket ship , v=.9c , u'(x)=(u(x)-v)/(1-vu'(x)/c^2)

not sure how to calculate u'(x) for the first rocket nor how to calculate u'(x) for the second rocket.
 
  • #4
u'(x)=u(x)-v/(1-v*u(x)/c^2)

This is the only formula you need... you want to see what the second rocket's speed is, in the first rocket's frame of reference... so if the first rocket is going at 0.9c relative to the earth, v=0.9c.

If the second rocket is going at -0.9c relative to the earth, then u(x)=-0.9c...

So just plug in u(x) and v into the equation for u'(x)... that gives you the speed of the second rocket as seen in the first rocket's frame of reference.
 
Last edited:

1. What is the Lorentz transformation in relativity theory?

The Lorentz transformation is a mathematical formula that describes how time, space, and other physical quantities change between two reference frames that are moving at a constant velocity relative to each other. It is a fundamental concept in the theory of relativity.

2. How is the Lorentz transformation used to calculate relativistic velocities?

The Lorentz transformation can be used to calculate the velocity of an object in one reference frame relative to another reference frame that is moving at a different velocity. This is necessary when dealing with objects moving at speeds close to the speed of light, where classical Newtonian mechanics no longer apply.

3. What is the difference between Galilean and Lorentz transformations?

Galilean transformations are the equations used in classical mechanics to describe the relationship between two reference frames that are moving at a constant velocity relative to each other. Lorentz transformations, on the other hand, are used in the theory of relativity to account for the effects of time dilation and length contraction at high velocities.

4. How does the Lorentz transformation affect time and space measurements?

The Lorentz transformation predicts that time will appear to pass slower and distances will appear shorter for an observer in one reference frame relative to an observer in another reference frame that is moving at a different velocity. This is known as time dilation and length contraction, respectively.

5. Can the Lorentz transformation be applied to all types of motion?

Yes, the Lorentz transformation can be applied to all types of motion, as long as the velocity is constant. It is a fundamental principle in the theory of relativity and has been experimentally verified in numerous experiments. However, it does not account for acceleration, which requires the use of more complex equations.

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