Question 935484: for the lovers of math:very very difficult algebra question:
A company manufactures high-powered fountains that can be used to create elaborate water shows set to light and music.The company makes three models of
fountains, each of which can launch a vertical stream of water to a different height, as indicated in the table below. Model A Model B Model C height 77 100 240 time to fall (s) 2.194, ----, ---- initial velocity 70.2 , ----, 123.9 complete the following tasks, filling in the missing values in the table as you find them: Find the time water would take to fall from each height in the table back to its starting level. Find the initial upward velocity required for fountain B to launch the water to its maximum height Create a function that will give you the minimum initial upward velocity ,v ,required to launch water to any given height , h. thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Model......... A Model .B Model C Model
height............. 77 ..100 ..240
time to fall (s) 2.194, ----, ----
initial velocity 70.2 , ----, 123.9
complete the following tasks, filling in the missing values in the table as you find them:
----
Formula::
height = -16*t^2 + vo*t
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A Model:: 77 = x*2.194^2 + 70.2*2.194
77 = -16*4.8136 + 154.019
77 = 77
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B Model::
Cannot solve for both time to fall and initial velocity;
one depends on the other
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C Model::
240 = -16t^2 + 123.9t
-----
Solve for "t" using the quadratic formula.
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Formula for minimum vo value::
Since h(t) = -16t^2 + vo*t
vo = (h+16t^2)/t = (h/t) + 16t
---
taking the derivative you get:
vo' = h*(-1/t^2) + 16
vo'= -h/t^2 + 16
Minimum vp will occur when (-h/t^2) + 16 = 0
Solving for "t" you get:
h/t^2 = 16
t^2 = 16h
t = 4sqrt(h)
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Cheers,
Stan H.
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