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Homework Help: Relative motion

  1. Nov 30, 2007 #1
    1. The problem statement, all variables and given/known data

    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. Relevant 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: AD=x=0,8c.t
    spaceship 1: DB=L-x=0,6c.t
    By addition
    L=AD+DB
    L=(0,8c+0,6c).t
    t=4,2.10^8/(1,4.3.10^8)
    t=1sec
    Is it ok so far?

    A hint to go on, please?
     
  2. jcsd
  3. Dec 1, 2007 #2
    The velocity of the spaceship 2 to the frame reference of the spaceship 1 is Uba=Ua+Ub=1.4c
    The velocity of the spaceship 1 to the frame reference of the spaceship 2 is also Uab=Ua+Ub=1.4c

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

    t=AB/Uab=4,2.10^8/(1,4.3.10^8)=1 sec

    Something is wrong. It cannot be the same.
     
  4. Dec 1, 2007 #3
    You don't consider the fact that the speeds are comparable to the speed of light.
     
  5. Dec 3, 2007 #4
    1. The problem statement, all variables and given/known data

    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. Relevant 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: AD=x=0,8c.t
    spaceship 1: DB=L-x=0,6c.t
    By addition
    L=AD+DB
    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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