Discovering Relativity: Calculating Spaceship Speed and Separation

[esb08]

Fun Relativity Question :)

Homework Statement

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?

Homework Equations

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

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

 

[Doc Al]

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

 

[esb08]

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

 

[Doc Al]

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

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.

 

[esb08]

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??

 

[Doc Al]

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)