Velocity of Separation in Special Relativity

[AGNuke]

An observer sees two spaceships flying apart with speed .99c. What is the speed of one spaceship as viewed by the other?

I considered two spaceships A and B. A is moving with velocity v_A in the left direction and B is moving with velocity v_B in the right direction. Hence, $v_{sep} = v_A + v_B = 0.99c$

Now finding the relative velocity of one spaceship with respect to other.

$$v_{rel} = \frac{v_A + v_B}{1 + \frac{v_Av_B}{c^2}}$$

Now since I don't know v_A or v_B, I can't find the answer. So, my question here is - is my question incomplete? Or is it possible to obtain an answer.

 

[dauto]

Your question is incomplete. you have the sum v_A+v_B but not the product. The product of two numbers cannot be obtained from their sum without some additional information.

 

[vela]

Maybe the question means to say each ship is traveling at 0.99c relative to the stationary observer in opposite directions.

 

[AGNuke]

Maybe the question means to say each ship is traveling at 0.99c relative to the stationary observer in opposite directions.

Hmm... I tried to look for the answer in the meantime, the book (Kleppner and Kolenkow) from which the question was lifted, fortunately provided it.

Taking your suggestion, the answer is coming out to be 0.99995c, which is the same as the answer provided.

Thanks a ton.

 

[HalfLostAndSearching]

I would say that the question is incomplete because we need to know the specific velocities of the two spaceships in order to calculate the relative velocity between them. Without knowing these values, it is not possible to accurately determine the speed of one spaceship as viewed by the other. Additionally, the concept of relative velocity in special relativity is more complex than just adding velocities, as shown in the equation above. It takes into account the effects of time dilation and length contraction, which would also need to be taken into consideration in order to accurately determine the relative velocity. Therefore, without more information, it is not possible to provide a definite answer to this question.