What is the initial speed of the water

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Homework Help Overview

The discussion revolves around determining the initial speed of water in a fountain that reaches a height of 560 feet. The context includes comparisons to other heights and the physics involved in projectile motion.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between height and initial speed, with one suggesting a formula involving distance and time. Others discuss the effects of gravity on speed and acceleration.

Discussion Status

The conversation includes various approaches to calculating initial speed, with some participants providing equations related to motion under gravity. There is no explicit consensus, but multiple perspectives on the problem are being explored.

Contextual Notes

Participants are considering the effects of gravity and acceleration on the speed of the water, with some noting that average speed may not accurately represent the situation due to changing conditions.

swatmedic05
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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
 

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