SOLUTION: Please help me solve this problem An object is projected upward from the top of the tower. it's distance in feet above the ground after t seconds is given by s(f)=-16t^2 +64t +

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please help me solve this problem An object is projected upward from the top of the tower. it's distance in feet above the ground after t seconds is given by s(f)=-16t^2 +64t +      Log On


   

Question 71246: Please help me solve this problem
An object is projected upward from the top of the tower. it's distance in feet above the ground after t seconds is given by s(f)=-16t^2 +64t +80. How many seconds will it take to reach ground level?
I would really like to know how to figure this out.
Thanks to anyone who is willing to help me
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
After t seconds, the height of an object with an initial upward velocity of v%5Bo%5D feet per second and an initial height of h%5Bo%5D feet is given by the function: s%28t%29+=+-16t%5E2%2Bv%5Bo%5Dt%2Bh%5Bo%5D
In your problem, v%5Bo%5D+=+64ft/sec and h%5Bo%5D+=+80ft, so you have:
s%28t%29+=+-16t%5E2%2B64t%2B80
You want to know at what time, t, will the height, h, be 0, so set the function s(t) = 0 and solve for t.
-16t%5E2%2B64t%2B80+=+0 You can simplify this a bit by factoring out -16.
-16%28t%5E2-4t-5%29+=+0 so:
t%5E2-4t-5+=+0 You can factor this quadratic equation.
%28t%2B1%29%28t-5%29+=+0 Apply the zero product principle.
t%2B1+=+0 and/or t-5+=+0
If t%2B1+=+0 then t+=+-1 Discard this solution as the time must be a positive value.
If t-5+=+0 then t+=+5
So the object will reach ground-level (h=0) in 5 seconds.