# Fun Relativity Question

1. Oct 4, 2008

### esb08

Fun Relativity Question :)

1. The problem statement, all variables and given/known data
two spaceships, A and B, are moving relative to the earth with speeds 4c/5 in opposite directions. What is the speed of the spaceship A according to an observer on B? According to an observer on B, how much does the separation of the spaceships increase in time of one second, as measured on his clock? According to an observer on the earth, how much does the separation increase in a time of one second as measured on his clock?

2. Relevant equations
lorentz transformation equations, v =v'+ u/(1+uv'/c^2)

3. The attempt at a solution
i used the velocity equation listed and plugged in the velocities for v' and u which were both 4c/5. i have no idea what to do for the other two questions. HELP please

2. Oct 4, 2008

### Staff: Mentor

Re: Fun Relativity Question :)

Hint: Make use of the basics: Distance = speed X time. If you solved the first question, you have all the speeds you need.

3. Oct 4, 2008

### esb08

Re: Fun Relativity Question :)

wait since the velocities are the same and in opposite directions does that mean the speed of A relative to B is 0??

4. Oct 4, 2008

### Staff: Mentor

Re: Fun Relativity Question :)

Forget relativity for a second and ask yourself if a relative speed of 0 makes sense. That would be true if they were moving in the same direction.

5. Oct 4, 2008

### esb08

Re: Fun Relativity Question :)

okay. i understand that. but using the equation v= v'+u/1 +(uv'/c^2) where v' is the velocity of B relative to the earth, u is the velocity of A relative to B, and v is the velocity of A relative to the earth then how would i switch around that equation to solve for u? wouldn't it be u=v-v'/1-(vv'/c^2)? so v and v' both equal 4c/5 and that gives me zero on the numerator so therefore u equals zero? where is my logic wrong??

6. Oct 4, 2008

### Staff: Mentor

Re: Fun Relativity Question :)

A more helpful version of the relativistic addition of velocity formula (for parallel velocities) might be:

$$V_{a/b} = \frac{V_{a/e} + V_{e/b}}{1 + (V_{a/e} V_{e/b})/c^2}$$

V_a/b = the speed of A with respect to B.

V_a/e = the speed of A with respect to the earth = -4c/5 (assume A goes left)

V_e/b = the speed of the earth with respect to B = -4c/5 (assume B goes right)