How long does a ball take to reappear at a certain point when it is thrown up?

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The discussion focuses on calculating the time it takes for a ball to reappear after being thrown upward outside a second-story apartment window. The ball is visible for 0.25 seconds while traveling 1.06 meters. To find the initial velocity, kinematic equations such as vf² = vi² + 2aΔx and x = xi + vit + 1/2 at² are suggested. The coordinate system can be adjusted to simplify calculations, treating the bottom of the window as the starting point. The analysis emphasizes the importance of considering forces acting on the ball and neglecting those that are insignificant.
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Homework Statement



Sitting in a second-story apartment, a physicist notices a ball moving straight upward just outside her window. The ball is visible for 0.25 s as it moves a distance of 1.06 m from the bottom to the top of the window.

How long does it take the ball to reappear?
What is the greatest height of the ball above the top of the window?

Homework Equations





The Attempt at a Solution

 
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What kinematic acceleration equations would you considered appropriate when describing a ball falling down from a two story building? What forces are acting upon the ball as it falls down? What forces would you consider negliglble in this scenario?
 
vf2 = vi2 + 2a\Deltax

x = xi + vit + 1/2 at2
 
Move your coordinate plane so the x-axis is on the bottom of the window. You can ignore everything that happens below the window, in fact you can pretend that the ball was launched right at the bottom of the window. You know that it took .25s to travel 1.06m so now just find Vo
 
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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