Relativistic kinematics.

In summary, the question asks for the speed of one spaceship as viewed by the other, given that they are both moving away from an observer with a speed of 0.99c in opposite directions. Using the equation for relative velocity, the speed is calculated to be 0.99995c.
  • #1
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An observer sees two spaceships flying apart with speed 0.99c, what is the speed of one spaceship as viewed by the other? the answer is: 0.99995c.

well we have the equation of relative velocity:
[tex]\frac{v_1+v_2}{1+\frac{v_1v_2}{c^2}}=0.99c[/tex]
now i think from the question that i need to find v1+v2 here, cause compared to spaceship 1, spaceship two is moving with speed -(v1+v2) and spaceship 1 compared to two is moving with speed v1+v2.

but how to find it, perhaps i need some algebraic manipulation which i don't see how do, or my above equations are flawed?
 
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  • #2
If I understand the situation correctly, you're seeing two spaceships moving exactly away from you with 0,99 c in opposite directions. Now you have to use the last equation on the following page: http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html with ux=0.99c and vx=-.99c o yield for the relative velocity (as viewed by either of the two spaceships:

[tex]w = \frac{|ux - vx| }{ 1 - ux vx/c^2}=\frac{2*0.99}{1-0.99^2}=0.99995[/tex]
 
  • #3
it should be 1+0.99^2 in the denominator.
thanks, i didn't undersatnd the situation, i thought that the observer measures the relative speed between them, and that speed is 0.99c.
 

1. What is relativistic kinematics?

Relativistic kinematics is the study of the motion and behavior of objects moving at speeds close to the speed of light. It is a branch of physics that combines the principles of special relativity and classical mechanics to describe the movement of particles and bodies in a high-speed environment.

2. How is relativistic kinematics different from classical kinematics?

Classical kinematics deals with the motion of objects at speeds much lower than the speed of light, while relativistic kinematics considers the effects of time dilation, length contraction, and the relativity of simultaneity at high speeds. It also uses different equations, such as the Lorentz transformations, to describe the motion of objects in a relativistic setting.

3. What is time dilation in relativistic kinematics?

Time dilation refers to the phenomenon where time appears to pass slower for an object moving at high speeds compared to an object at rest. This is a consequence of special relativity, where time is relative and can be affected by the speed of an object. The faster an object moves, the slower time appears to pass for that object.

4. How does relativistic kinematics apply to particle accelerators?

Particle accelerators, such as the Large Hadron Collider, use relativistic kinematics to accelerate particles to high speeds and energies. The principles of special relativity and relativistic kinematics are essential for calculating the trajectories and interactions of particles at these high speeds, and for predicting the results of collisions between particles.

5. What are some real-world applications of relativistic kinematics?

Relativistic kinematics has many practical applications, such as in space travel, where spacecraft must travel at high speeds to reach distant destinations. It is also crucial in the development of technologies like GPS, which rely on the precise synchronization of clocks in satellites moving at high speeds. Additionally, relativistic kinematics is used in medical imaging techniques, such as PET scans, to account for the effects of time dilation on the decay of radioactive isotopes.

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