How can the Equations of Motion be used to calculate missing parameters?

AI Thread Summary
The discussion focuses on using the equations of motion to solve for missing parameters when only a few values are provided. Participants express confusion about how to proceed with calculations when not all four necessary variables (displacement, time, initial velocity, final velocity) are known. A suggestion is made to create a system of two equations to help find the missing parameters. This method can simplify the problem and provide a clearer path to the solution. Understanding how to manipulate these equations is crucial for accurate calculations in physics.
staceyw
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Can someone please explain what you are supposed to do when you are only give two or three of the things (eg displacement or time) when you need four, how are you supposed to work it out then? :bugeye: it seems to be very confusing! :confused:
I am really confused and need help! Thanks :smile:
 
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I would suggest making a system with two different equations.
 
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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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