SOLUTION: 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)

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 + 14 t + 30
I don't understand part b or c
b. when will the stone reach it's highest elevation
c.when will the stone hit the ground?
I would really appreciate any help I can recieve.
Thank you very much
please help soon!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
:
I don't understand part b or c
b. when will the stone reach it's highest elevation
:
It will reach the highest point (max) on the axis of symmetry
Find the axis of symmetry using the formula: x = -b/(2a)
:
In this problem x=t, a=-4.9, b=14, we have:
t =
t =
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
:
Solve for t using the quadratic formula: a=-4.9, b=14, c=30
:
You should get a positive solution of about 4.28 seconds
:
:
A graph of this:

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