Reviewing Responses to Motion and Forces Questions

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The discussion focuses on reviewing answers to motion and forces questions, with a request for feedback on the provided solutions. The reviewer notes that the interpretation of the first problem may be incorrect, suggesting a different understanding of when the second arrow reaches the first. Additionally, they recommend a more direct method for calculating the clown's flight time using a quadratic equation instead of a two-step approach. Overall, the reviewer acknowledges that the original approach to the problems appears to be on the right track. Clear guidance on interpretation and method improvement is provided.
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Can someone check to see if I am on the right track as far as these questions go? I have place the questions and my answers in an attachment. Thanks!
 

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I didn't check all of your math, but the approach looks fine. I do have a couple of comments:

1) In problem 1, I'd interpret the question differently. You found the initial speed of the second arrow if it reached the first at the peak of its flight. This is, I'll grant you, halfway through the flight of the arrow, but it seemed to me that the question meant that the second arrow reached the first when the first was halfway up to its peak.

2) You could have gotten the time of the clown's flight directly instead of in two steps by using a vertical displacement of two meters. You'd have had a quadratic to solve which would have given you two times - one going up, and one going down. Inspection (basically, looking at it) would give you the time when he hit the net.

As I said, though, you seem to be approaching them correctly.
 
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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