Calculating Ball Trajectory from Window Observations

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The discussion focuses on calculating the trajectory of a ball observed moving upward from a second-story window. The ball is visible for 0.25 seconds while traveling 1.05 meters. Participants identify the motion as one-dimensional in the vertical direction, applying relevant equations of motion, including those involving initial velocity and acceleration due to gravity. The initial height is set to zero at the bottom of the window, allowing for calculations of initial velocity and time until the ball reappears. The conversation emphasizes using kinematic equations to solve for the ball's maximum height and reappearance time.
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Sitting in a second-story apartment, a physicist notices a ball moving straight upward just outside his/her window. The ball is visible for 0.25s as it moves a distance of 1.05m from the bottom to the top of the window. a) How long does it take before the ball reappears? b) What is the greatest height of the ball above the top of the window?

Hey, I don't know how to approach these types of problems. Help?
 
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What type of motion is it?
What equations apply to that type of motion?
 
It's one dimensional motion in the y direction. And, I think the equations that apply are:

d = v(initial)t + (0.5)at^2

v(final)^2 = v(initial)^2 + 2ad
 
Do you know the value of a in these equations?
 
Yeah, a = g.
 
d = v(initial)t + (0.5)at^2
should enable you to find something. Take time zero to be when the ball first appears, and call that initial height zero, too. You should then be able to put in numbers for the ball at the top of the window and then solve for the initial velocity at the bottom of the window.

Finally, use the same equation again to figure out the answer to the first question.
 
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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