Collision time between two rockets in one rocket's frame....

[Apashanka]

Homework Statement:

length contraction

Relevant Equations:

$L_0=\gamma L_{moving}$

While attempting this question ,
velocity of $B$ wrt $A$ ,$u'_x=\frac{u_x-v}{1-u_xv/c^2}$ where $u_x=-0.6c,v=0.8c$ comes out to be $-0.945c$ (approaching)..
The distance between $A$ and $B$ seen by $A$ at $t=0$ is $d=\sqrt(1-.8^2)4.2×10^8$ comes out to be $252*10^6m$
Therefore collision time seen in $A's$ frame is $d/0.945c$ which is 0.888(x=8.8) but the ans is given x=6??
Can anyone please help me in picking the mistake...
Thanks

 

[PeroK]

How long do the rockets take to collide in the Earth frame?

 

[PeroK]

Homework Statement:: length contraction
Relevant Equations:: $L_0=\gamma L_{moving}$

View attachment 262248

The distance between $A$ and $B$ seen by $A$ at $t=0$ is $d=\sqrt(1-.8^2)4.2×10^8$ comes out to be $252*10^6m$

Your mistake is to use length contraction without thinking about it. You could use the Lorentz Transformation to see that this calculation is wrong.

 

To use the length contraction formula you need to have first established that the two "endpoints" of the length you are measuring are both at rest in some inertial frame of reference. That's not the case here.