Relativity Problem: Find Passenger Speed Relative to Bank

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The problem involves calculating the speed of a passenger walking diagonally on a ferry boat moving away from a riverbank. The ferry travels at 3 km/h, the river flows at 4 km/h, and the passenger walks at 1.39 m/s at an angle of 53.1 degrees upstream. The discussion suggests that the speeds are too low for relativistic effects, indicating that vector addition is the appropriate method for solving the problem. Participants clarify that a straightforward approach rather than Lorentz transformations is needed to find the passenger's speed relative to the bank. The focus remains on correctly applying vector addition to determine the final speed.
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Homework Statement



A ferry boat headed directly away from the river bank is traveling at 3 km/h with respect to the water in a river flowing at 4 km/h. A passenger walks diagonally toward the stern of the boat with a speed of 1.39 m/s. The passenger's path is at an angle of 53.1 degrees toward the upstream direction from the length of the boat. What is the passenger's speed relative to the bank?

Homework Equations



v'=(u+v)/(1+(u*v)/c^2)

The Attempt at a Solution



I know the speeds form a triangle with leg lengths 3 and 4 and hypotenuse 5. I'm not sure where to go from there, though...
 
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It looks like you might have to use 2 lorentz transformations. First, i would set up my rest frame, S, to be the water, and the moving S' frame to be the boat. I would then find the velocity of the person in the reference frame of the water, S. I would then use the lorentz transformations again, setting my new rest frame to be the bank and my moving frame to be the water. This way you willk now the velocity of the person relative of the water and will be able to transform it to the bank. this might be wrong though -- my spec rel is not great.
 
bfr said:
… 3 km/h … 4 km/h … 1.39 m/s …

Hi bfr! :smile:

erm … are you sure this is a relativity question? :confused:

The speeds are far too small for relativity to be relevant … I think you're expected to treat it as a straightforward vector addition problem. :smile:
 
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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