Solve Free Falling Object: Find Height of Ball

AI Thread Summary
A ball dropped from rest covers three-fifths of the distance to the ground in the last second of its fall, prompting a calculation of the initial height. The user initially struggled with kinematic equations to derive the height but was unable to find the correct answer after extensive effort. Eventually, the user resolved the problem independently without needing further assistance. The discussion highlights the challenges of applying kinematic equations in free-fall scenarios. Ultimately, the user successfully determined the height from which the ball was dropped.
Casimi
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Homework Statement


A ball, dropped from rest, covers three-fifths of the distance to the ground in the last second of its fall. From what height was the ball dropped?

The Attempt at a Solution


I have spent the past thirty minutes attempting to figure this out. I initially used a kinematic equation which gave me a new expression for the height and I attempted to put that expression into another kinematic equation but I still cannot seem to arrive at the correct answer.

Any advice or help on this would be appreciated!
 
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No need, I finally figured it out :)
 
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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Thread 'Struggle to understand the concept of the question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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