What is the initial speed of the water

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The discussion focuses on calculating the initial speed of water in the world's highest fountain, which reaches 560 feet. To determine this speed, the equations of motion are applied, considering gravity's effect on the water's ascent and descent. The initial speed can be derived from the formula v^2 = (v0)^2 - 2gd, where g represents gravitational acceleration and d is the height. It is noted that the speed of the water varies due to gravitational influence. Understanding these principles is essential for accurately calculating the initial speed of both the fountain water and an object thrown to the same height.
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The world's highest fountain of water is located, appropriately enough, in Fountain Hills, Arizona. The fountain rises to a height of 560 (5 feet higher than the Washington Monument).

What is the initial speed of the water
 
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what would be initial speed of the ball someone throws to a height of 560 feet?
 
total distance/total time
 
That would be average speed. Speed of water isn't same all the time, it's slows down because of gravity. Distance moved with constant acceleration is:
d = v0*t-1/2*a*t^2, v0 is initial speed, a - a negative acceleration and t -time. Speed is:
v = v0 - at. You can solve those two equations for initial speed, and get:
v^2 = (v0)^2 - 2gd
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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