SOLUTION: a stone is thrown upward from a bridge. the stones height s(t) in ft, above the water t seconds after the stone is thrown is given by the function s(t)=-16t^2+32t+256. a. find

Question 966364: a stone is thrown upward from a bridge. the stones height s(t) in ft, above the water t seconds after the stone is thrown is given by the function s(t)=-16t^2+32t+256.
a. find the max height of stone.
got 272 ft.
b. find the time it takes the stone to hit the water?
need help with this one.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
a stone is thrown upward from a bridge. the stones height s(t) in ft, above the water t seconds after the stone is thrown is given by the function s(t)=-16t^2+32t+256.
a. find the max height of stone.
s(t)=-16t^2+32t+256
complete the square:
s(t)=-16(t^2-2t+1)+16+256
=-16(t-1)^2+272
This is an equation of a parabola that opens downward with vertex at (1, 272)
stone reaches maximum height of 272 ft, 1 sec after it is thrown.
..
b. find the time it takes the stone to hit the water?
when stone hits the water, s(t), height=0
-16t^2+32t+256=0
t^2-2t-16=0
use quadratic formula to solve for t

a=1, b=-2, c=-16
ans:
t=5.12 sec
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