Why am I having trouble solving for 005 in the Velocity Dilemma 004 & 005?

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The user successfully solved for problem 004, obtaining a change in velocity of 12.972, but is struggling with problem 005. They initially attempted to use a kinematics equation but received an incorrect result for Vb, which was 11.57559. A response pointed out that the equation used was meant for finding initial velocity, which is not applicable in this case. The user is encouraged to reassess their approach based on this clarification. Understanding the correct application of kinematics is crucial for solving the problem accurately.
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I have solved 004 and got 12.972 as the change in velocity. I am having a little difficulty solving for 005. Initially I thought I could use the x=(1/2)(2.35)(5.52)^2+Vb(5.52) kinematics equation, but for some reason it's not right. The answer I got with my attempt was Vb =11.57559. Am I not supposed to use kinematics in this situation? What am I doing wrong?
 
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Hi Garen,

Garen said:
34hxton.jpg




I have solved 004 and got 12.972 as the change in velocity. I am having a little difficulty solving for 005. Initially I thought I could use the x=(1/2)(2.35)(5.52)^2+Vb(5.52) kinematics equation, but for some reason it's not right. The answer I got with my attempt was Vb =11.57559. Am I not supposed to use kinematics in this situation? What am I doing wrong?


If you compare the equation you are using with the one in your book, you'll see that the unknown in that equation represents the initial velocity, which is not what you want. Do you see what to do now?
 
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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