Events occuring in 4D spacetime

AI Thread Summary
The discussion revolves around confusion regarding the application of the Lorentz transformation formula, specifically in determining the ct' axis. It is clarified that the formula ct' = γ(ct - (v/c)x) is not used to find the ct' axis directly, but rather to find the x' axis, where ct' = 0. The misunderstanding stems from the relationship between ct and x in the context of the transformation. The key point is that the Lorentz formula serves to relate coordinates in different inertial frames, emphasizing the distinction between ct and ct'. Understanding this distinction is crucial for solving related problems in 4D spacetime.
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Homework Statement
Please see below
Relevant Equations
Please see below
For this problem and solution,
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I'm confused by part (c) and (d). I don't understand how the Lorentz formula ##ct' = \gamma (ct - \frac{v}{c}x)## can be used to find the ##ct'## axis. This is because they found the ##ct = \frac{v}{c}x## which is in terms of ##x## not ##x'##. Does anybody else please see this subtle bit here?

Thanks!
 
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ChiralSuperfields said:
Homework Statement: Please see below
Relevant Equations: Please see below

I don't understand how the Lorentz formula ct′=γ(ct−vcx) can be used to find the ct′ axis.
It cannot. It is used to find the x’ axis - which by definition is ct’ = 0.
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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