SOLUTION: An object is thrown downward from a plane which is 540 feet above the ground. The object is thrown with an initial velocity of 27 ft/sec. The distance traveled by the object in t s

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: An object is thrown downward from a plane which is 540 feet above the ground. The object is thrown with an initial velocity of 27 ft/sec. The distance traveled by the object in t s      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 311559: An object is thrown downward from a plane which is 540 feet above the ground. The object is thrown with an initial velocity of 27 ft/sec. The distance traveled by the object in t seconds is s = 16t2 + 27t, where s is in feet. How long does it take the object to reach the ground? Show your work.
I need help i understand that
540 = 16t^2 + 27t but what is after this I am lost. Please help me if you can
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
540 = 16t^2 + 27t
Considering up to be positive, it's
h(t) = -16t^2 - 27t + 540 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B-27x%2B540+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-27%29%5E2-4%2A-16%2A540=35289.

Discriminant d=35289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+35289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+35289+%29%29%2F2%5C-16+=+-6.71417707666998
x%5B2%5D+=+%28-%28-27%29-sqrt%28+35289+%29%29%2F2%5C-16+=+5.02667707666998

Quadratic expression -16x%5E2%2B-27x%2B540 can be factored:
-16x%5E2%2B-27x%2B540+=+%28x--6.71417707666998%29%2A%28x-5.02667707666998%29
Again, the answer is: -6.71417707666998, 5.02667707666998. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B-27%2Ax%2B540+%29