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

In summary, the collision time seen in ##A's## frame is 0.888 (x=8.8), but the correct answer is x=6. The mistake is using length contraction without considering the motion of the endpoints in an inertial frame.
  • #1
Apashanka
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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
 
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  • #2
How long do the rockets take to collide in the Earth frame?
 
  • #3
Apashanka said:
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.
 
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  • #4
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.
 
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1. What is the meaning of "collision time between two rockets in one rocket's frame"?

"Collision time between two rockets in one rocket's frame" refers to the amount of time it takes for two rockets to collide with each other, as measured from the perspective of one of the rockets.

2. How is the collision time between two rockets calculated?

The collision time between two rockets can be calculated using the relative velocity between the two rockets and the distance between them. This can be done using the equation t = d/v, where t is the collision time, d is the distance between the two rockets, and v is their relative velocity.

3. Does the mass of the rockets affect the collision time?

Yes, the mass of the rockets can affect the collision time. Heavier rockets will have a greater momentum and may take longer to collide, while lighter rockets will have a lower momentum and may collide faster.

4. How does the speed of the rockets affect the collision time?

The speed of the rockets does affect the collision time, as it is a factor in calculating the relative velocity between the two rockets. The faster the rockets are moving, the shorter the collision time will be.

5. Can the collision time between two rockets be altered?

The collision time between two rockets can be altered by changing the relative velocity between them. This can be done by adjusting the speed or direction of one or both of the rockets. Other factors such as air resistance and gravitational forces may also affect the collision time.

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