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Water is spraying from a nozzle in a fountain forming a parabolic as it travels. The nozzle is 10cm above the surface of the water. The water achieves maximum height of 100cm above the water surface and lands in the pool. The water spray is again 10cm above the surface of the water when it is 120cm horizontally from the nozzle. Origin is at the surface of water directly below the nozzle. I got -1/4(x-60)^2 + 100 but the answers say k supposed to be 90? Can someone explain how origin works

 Mar 23, 2021
edited by zjqson  Mar 23, 2021
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Water is spraying from a nozzle in a fountain forming a parabolic as it travels. The nozzle is 10cm above the surface of the water. The water achieves maximum height of 100cm above the water surface and lands in the pool. The water spray is again 10cm above the surface of the water when it is 120cm horizontally from the nozzle. Origin is at the surface of water directly below the nozzle. I got -1/4(x-60)^2 + 100 but the answers say k supposed to be 90? Can someone explain how origin works

 

I decided to start with the origin (0,0) at the point that will become  (60,10) later on.

 

the height of the water jet is 90 units above the axis, and it crosses the x axis at =+/- 60

 

so

y=k(x-60)(x+60)

sub in (0,90) and I get 

90=k(-3600)

k=-1/40

 

so far the equation is    \(y=\frac{-1}{40}(x^2-3600)\)

 

Now I have to translate it into the correct position

 

\(y-10=\frac{-1}{40}((x-60)^2-3600)\\ \)

 

you can finish it.

 

Here is a link to the graph

https://www.desmos.com/calculator/jelcjtjsso

 Mar 23, 2021

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