SOLUTION: If an object is projected vertically upward from an altitude of s(o) feet with an intial velocity of v(o) ft/sec, then its distance above the ground after t seconds is: s(t)=-16t^2

Question 372684: If an object is projected vertically upward from an altitude of s(o) feet with an intial velocity of v(o) ft/sec, then its distance above the ground after t seconds is: s(t)=-16t^2+ v(o)t+ s(o).
If s(1)= 64 and s(2)=66, what are s(o) and v(o)?
I honestly do not know how to set the problem up! Please help, it would be greatly appreciated!Thanks :)

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Given:
s(t)=-16t^2+ v(o)t+ s(o).
If s(1)= 64 and s(2)=66, what are s(o) and v(o)?
.
So,
when x=1 then s(1)=64
and
when x=2 then s(2)=66
.
From here, you now have two unknowns and two equations:
when x=1 then s(1)=64
s(t)=-16t^2+ v(o)t+ s(o)
s(1)=-16(1)^2+ v(o)(1)+ s(o)
64=-16+ v(o)+ s(o)
89=v(o)+ s(o) equation 1
.
when x=2 then s(2)=66
s(t)=-16t^2+ v(o)t+ s(o)
s(2)=-16(2)^2+ v(o)(2)+ s(o)
66=-16(4)+ 2v(o)+ s(o)
130=2v(o)+ s(o) equation 2
.
Considering the "system of equations" then:
130=2v(o)+ s(o)
89=v(o)+ s(o)
.
Multiply both sides of the bottom equation by -1 and add:
130=2v(o)+ s(o)
-89=-v(o)- s(o)
---------------------
41 ft/sec = v(0)
.
Substitute the above into:
89=v(o)+ s(o)
89=41+ s(o)
48 feet = s(o)
RELATED QUESTIONS
If an object is projected vertically upward from an altitude of a feet with an initial... (answered by mananth,stanbon)

Need help setting up this equation. If an object is projected vertically upward from an... (answered by solver91311,josmiceli)

If an object is projected vertically upward from an altitude of s0 feet with an initial... (answered by ankor@dixie-net.com)

If an object is projected vertically upward from an altitude of s0 feet with an initial... (answered by Alan3354)

If an object is projected vertically upward from ground level with an initial velocity of (answered by richwmiller)

If an object is projected vertically upward from ground level with an initial velocity of (answered by MathLover1,josmiceli)

If an object is projected vertically upward from ground level with an initial velocity of (answered by Boreal,josmiceli)

An object is projected vertically upward with an initial velocity of Vo ft/sec, and its... (answered by stanbon)

An object is projected vertically upward from the top of a building with an initial... (answered by josmiceli,amalm06)