Calculating Ice Cube Landing Points Using Galilean Relativity

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2 trains are traveling at constant speeds on 2 parralel straight line. The first A is traveling at 5m/s the second B is traveling at 2 m/s. An observer at the station observes both trains. At a given instant of time, a passenger in A, a passenger in B and the observer at the sation are all aligned along a line normal to the motion of the trains. At that point, a passenger in A drops an ice cube from his drink which he is holding at a height of 1.40m. Using Galilean relativity where will the ice cube land as far as each observer is concerned?

I worked out for A to be x' + u't' = 0 as u' = 0 as there is no horizontal velocity of ice cube relative to A.

Im not sure of the formula to work out B and for ground observer can someone help?

 

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any ideas would be useful, I am not sure whether I am expected to work out the time of how long it will take for the ice cube to land using the distance 1.4 m and gravity?

 

[Daverz]

Yes, they expect you to work out the time using gravity and the initial height of the cube, then use Galilean coordinate transformations on this (you could also work out the problems with the cube having an initial velocity equal to the relative velocities, but it sounds like they want you to explicity start with a Galilean transformation, so that you get a feel for how to use Lorentz transformations later on).

 

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any ideas anyone?

 

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is my method for the asnwer for observer A correct??