Special Relativity: spaceships heading toward each other

[Sidsid]

Homework Statement

So, the problem is this: two spaceships are heading to a bar located exactly between the spaceships, one approaches from the left, the other from the right. They are both moving with a speed of 0.8c. So in the bar's point of view they meet at the bar. Where do they meet in the left ship's view, at the bar , left of the bar or right
?

Relevant Equations

$V_ab= (v_bc+ v_ac)/(1+ (v_bc*v_ac)/c^2) $

In the left point of view the bar is approaching at 0.8c and the other space ship at something very near c (Einsteins velocity addition rule). To reach the left ship the other ship has to bridge double the distance of the bar with less than double the speed of the bar. Therefore they meet right of the bar. But this seems very counterintuitive. The meeting of the spaceships is an event with a time and a place, and I remember something of spacetime events being "immune to such trickery". What is right?

 

[Ibix]

If they meet at the bar, is it possible that they also don't meet at the bar? Say they actually collide with and destroy the bar. Which ship(s) would be damaged if they meet at the bar or left or right of the bar?

Have you been taught the Lorentz transforms? If so, start in the rest frame of the bar and write down the coordinates of the ships 1s before they meet and when they meet (hint: make this last event the origin to save yourself some maths). Transform to the rest frame of one of the ships. What do you notice about the time coordinates of the ships' start events?

 

[anuttarasammyak]

The three meet is an event, a point in space time. It is shared with any coordinates as you suspect.

[EDIT]I interpreted that they meet at a point. Bar has length. If OP means the two rockets meet the bar at different points, it is another story.

 

[Orodruin]

The problem is completely conceptual. No computations are needed and you are given the answer:

they meet at the bar

This is an invariant statement as it is a statement about a particular event (the meeting) occurring on the world line of the bar.

 

[kuruman]

They may meet at the bar, but I betcha their drinks will not arrive simultaneously.

 

[Mister T]

To reach the left ship the other ship has to bridge double the distance of the bar with less than double the speed of the bar.

Okay.

Therefore they meet right of the bar.

I don't see how that follows. In the bar's rest frame each ship is the same distance away at any given time. But those two events will not be simultaneous in the left ship's rest frame!

 

[Sidsid]

Thank you all for your help! I understand now.

 

[SammyS]

They may meet at the bar, but I betcha their drinks will not arrive simultaneously.

Yes, I think I've been to that bar.