Question 171929
suppose that an object is thrown into the air with an intial upward velocity of vo meters per second from a height ho meters above the ground. Then t seconds later, its height h(t) meters above the ground is modeled by the function h(t)= -4.9 t^2 + vot + ho. (this model dosent' account for resistance)

if a stone is thrown with an upward velocity of 14 m/s from a cliff 30 meters high
I answered part a which asked:
a. find its height above the ground t seconds later.
h(t)= -4.9t^2 + 14t + 30
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I don't understand part b or c
b. when will the stone reach it's highest elevation
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It will reach the highest point (max) on the axis of symmetry
Find the axis of symmetry using the formula: x = -b/(2a)
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In this problem x=t, a=-4.9, b=14, we have:
t = {{{(-14)/(2*-4.9)}}}
t = {{{(-14)/(-9.8)}}}
t = +1.43 seconds, it will be at it's highest point
:
:
c.when will the stone hit the ground? 
;
When it hits the ground h(t) = 0, find t: we have;
-4.9t^2 + 14t + 30 = 0
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Solve for t using the quadratic formula: a=-4.9, b=14, c=30
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You should get a positive solution of about 4.28 seconds
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:
A graph of this:
{{{ graph( 300, 200, -1, 5, -10, 50, -4.9x^2+14x+30) }}}