• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • Thread starter Apashanka
  • Start date
  • #1
429
15

Homework Statement:

length contraction

Relevant Equations:

##L_0=\gamma L_{moving}##
Screenshot_20200507-114128~2.png

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
 

Answers and Replies

  • #2
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
13,421
5,935
How long do the rockets take to collide in the Earth frame?
 
  • #3
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
13,421
5,935
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.
 
  • Like
Likes Apashanka and etotheipi
  • #4
etotheipi
2019 Award
1,781
908
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.
 
  • Like
Likes Apashanka and PeroK

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

  • Last Post
Replies
7
Views
2K
Replies
7
Views
879
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
4
Views
146
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
3
Views
8K
Replies
3
Views
564
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
18
Views
1K
  • Last Post
Replies
3
Views
1K
Top