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)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> 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)      Log On


   

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) About Me  (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 = %28-14%29%2F%282%2A-4.9%29
t = %28-14%29%2F%28-9.8%29
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:
+graph%28+300%2C+200%2C+-1%2C+5%2C+-10%2C+50%2C+-4.9x%5E2%2B14x%2B30%29+