# Special Relativity and Relative motion

1. Homework Statement

An observer on Earth sees two spaceships moving in opposite directions and finally they collide. At t=0 the observer on Earth says that the spaceship 1 which moves to the right with Ua=0.8c is at the point A and the spaceship 2 which moves to the left with Ub=0.6c is at the point B. The distance AB=L=4,2.10^8 m.
When do the two spaceships collide to the earth frame of reference?
What is the velocity of the spaceship 2 to the frame reference of the spaceship 1?
What is the velocity of the spaceship 1 to the frame reference of the spaceship 2?
When does the collision happen to the frame reference of the spaceship 1 and to the frame reference of the spaceship 2?

2. Homework Equations

3. The Attempt at a Solution

Let D be the point of the collision and AD=x, so DB=L-x
The velocity is constant.
spaceship 1: DB=L-x=0,6c.t
L=(0,8c+0,6c).t
t=4,2.10^8/(1,4.3.10^8)
t=1sec
Is it ok so far?

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Shooting Star
Homework Helper
So far, correct.

The velocity of the spaceship 2 to the frame reference of the spaceship 1 is the same as the velocity of the spaceship 1 to the frame reference of the spaceship 2.

Shooting Star
Homework Helper
Numerically, yes. Opp signs because in opp directions. But that shouldn't bother you.

Using Lorentz transformations

0,8c=(U21-0,6c)/(1-U21.0,6c/c^2)

U21=1,4c/1,48

Correct?

When does the collision happen to the frame reference of the spaceship 1 and to the frame reference of the spaceship 2?

Now we must use Lorentz transformation for the length?

Shooting Star
Homework Helper
Using Lorentz transformations

0,8c=(U21-0,6c)/(1-U21.0,6c/c^2)

U21=1,4c/1,48

Correct?
(Is your keyboard very old, so you can't tell the , from the .? Just kidding...)

Yes. You could have got it also by (0.8+0.6)c/(1+0.8*0.6).

Shooting Star
Homework Helper
When does the collision happen to the frame reference of the spaceship 1 and to the frame reference of the spaceship 2?

Now we must use Lorentz transformation for the length?
The question is "when", not where. So, use the formula for time.

Thank you very much for your time.