SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the ne

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The height h in feet of an object after t seconds is given by the function h = –16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the ne      Log On


   

Question 124223: The height h in feet of an object after t seconds is given by the function
h = –16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The height h in feet of an object after t seconds is given by the function
h = –16t^2 + 30t + 3. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.
:
When it hits the ground h = 0, therefore:
:
-16t^2 + 30t + 3 = 0
:
Using the quadratic formula:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem; a=-16, b=30, c=3
t+=+%28-30+%2B-+sqrt%2830%5E2+-+4+%2A-16+%2A+3+%29%29%2F%282%2A-16%29+
:
t+=+%28-30+%2B-+sqrt%28900+-%28-192%29+%29%29%2F%28-32%29+
:
t+=+%28-30+%2B-+sqrt%28900+%2B+192+%29%29%2F%28-32%29+
:
t+=+%28-30+%2B-+sqrt%281092%29%29%2F%28-32%29+
:
Two solutions:
t+=+%28-30+%2B+33.0454%29%2F%28-32%29
:
t+=+%283.0454%29%2F%28-32%29
:
t = -.095; not a solution
and
t+=+%28-30+-+33.0454%29%2F%28-32%29
:
t+=+%28-63.0454%29%2F%28-32%29
:
t = +1.970 seconds to hit the ground
:
:
You can substitute this value for t in the original equation and confirm
that it does, in fact, = 0, or very close to it