SOLUTION: Hello, I am having problems with one of my algebra 2 questions. It says that I need to create a function that will give me the minimum initial upward velocity, v, required to launc

Question 1066608: Hello, I am having problems with one of my algebra 2 questions. It says that I need to create a function that will give me the minimum initial upward velocity, v, required to launch water to any given height.
Previously, I solved the first part of it using the vertical motion formula and got V=16t+h/t, but the formula is not the minimum velocity, so I need help figuring out the steps to find that out. I don't want the answer, but rather a point in the right direction.
Thank you in advance!
Found 3 solutions by josmiceli, Alan3354, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Launching against gravity from ground level,

Units are feet and seconds. The 1st term is the
effect of gravity. The 2nd term is the effect of
launch speed. I can solve for
--------------------------------------

I'm not sure what they mean. would be
minimum velocity needed to launch to at least
-----------------------------------------------
If you plot as a variable on the y-axis, and
on the horizontal axis, and remains fixed,
( no longer )
then you have a function with a minimum.
I'll do a plot with

Every point on the curve is ( t, v[0] ) that will let me
reach ft.
----------------------
This is my attempt to figure out what they
mean by minimum velocity. By all means get
other input on this

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
create a function that will give me the minimum initial upward velocity, v, required to launch water to any given height.
---------------
The speed to launch something upward to a height is the same as the impact speed of something dropped from that height.
---
s = at^2/2 = 16t^2 -- s in feet, t in seconds.
---
t = sqrt(s/16) = sqrt(s)/4
v = at = 32t

Or if you prefer

Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
.
On objects launched upward see the lessons
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Projectiles launched/thrown and moving vertically up and down".

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