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Lissajoux
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Homework Statement
A spaceship leaves Earth at 12 noon. At that time the spaceship clock is set to be synchronised with Earth time. It travels through space in a straight line at a constant speed 0⋅60 c.
A radio signal is sent to the spaceship from Earth at 2pm.
A shuttle is launched from the Earth at 4pm and travels directly towards the spaceship at a constant speed of 0⋅80 c.
a) In the Earth frame of reference, relative to the spaceship what are:
i. the speeds of the radio message and of the shuttle.
ii. the corresponding times in Earth frame for the arrival at the spaceship of the radio message and of the shuttle.
b) In the spaceship frame of reference:
i. at what times did the signal and the shuttle leave the Earth?
ii. what are the speeds of the signal and of the shuttle?
iii. what are the times for the radio message and for the shuttle to arrive at the spaceship?
Homework Equations
Within the problem statement and solution attempt.
The Attempt at a Solution
In this question can ignore the acceleration periods and all gravitational effects.
Really not sure how to go about this, but this is what I have so far:
a) [itex]v=0.6c=1.8\times 10^{8}ms^{-1} , u_{x}=c=3\times 10^{8}ms^{-1}[/itex]
i. use equation:
[tex]V=\frac{u_{x}v}{1+\frac{u_{x}v}{c^{2}}}[/tex]
therefore:
[tex]V_{signal}=3\times 10^{8}ms^{-1}[/tex] and [tex]V_{shuttle}=2.838\times 10^{8}ms^{-1}[/tex]
ii. Not sure how to do this, i.e. what equations to use. Assume I need to use the results from part i. somehow.
b) At the moment I'm unsure how to adapt the calculations to take into account the dilations resulting from being in the spaceship's frame of reference. Some advice here would be great to get me going with this part.