Solving Momentum Questions: Find Post Explosion Speed of Cannon & Ball

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AI Thread Summary
To solve the problem of finding the post-explosion speed of a cannon and a tennis ball, the key concepts of momentum and impulse are essential. The discussion emphasizes the need to identify relevant equations, particularly those related to conservation of momentum, which is fundamental in physics. Participants encourage the individual to recall and apply the equations learned in introductory physics courses, highlighting the importance of understanding these principles. The conversation stresses that without knowing the appropriate equations, it is challenging to grasp the concepts of momentum and impulse effectively. Understanding these equations is crucial for accurately determining the speeds of both the cannon and the tennis ball post-explosion.
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Homework Statement



A 56.2 gram tennis ball is loaded into a 1.27 kg homemade cannon. the cannon is at rest when it is ignited immediatly after the impulse of the explosion, a photo gate timer measures the cannon to recoil backwards a distance of 6.1 cm in 0.0218 seconds. determine the post explosion speed of the cannon and of the tennis ball

Homework Equations



i don't know equation

The Attempt at a Solution



confused can someone explain to me if they get this problem
 
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We get the problem but you haven't even bothered to say what equations are relevant.
 
Sure you do--You would have already seen that equation by now in a general physics course, quite a few times by now. One of the first equations you are taught in intro physics class. What equation uses some of the information that you've already been given in your problem?? How is it written?? Show us that first and tell us what you get. If you don't know what equation to use for starters then how can we expect that you understand momentum/impulse? Show the equation, and tell us what you understand (or what you think you understand) about impulse and momentum.
 
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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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