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 263334: 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?

Found 2 solutions by richwmiller, nerdybill:
Answer by richwmiller(17219) About Me  (Show Source):
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
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?
First, determine how long it will take to fall to the ground.
.
Given:
s = 16t^2 + 27t
Set s to 540 and solve
540 = 16t^2 + 27t
0 = 16t^2 + 27t - 540
Solve using the quadratic equation. Doing so, yields:
t = {5.0, -6.7}
Throw out the negative answer leaving:
t = 5 seconds
.
Details of the quadratic equation to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B27x%2B-540+=+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=%2827%29%5E2-4%2A16%2A-540=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-%2827%29%2Bsqrt%28+35289+%29%29%2F2%5C16+=+5.02667707666998
x%5B2%5D+=+%28-%2827%29-sqrt%28+35289+%29%29%2F2%5C16+=+-6.71417707666998

Quadratic expression 16x%5E2%2B27x%2B-540 can be factored:
16x%5E2%2B27x%2B-540+=+16%28x-5.02667707666998%29%2A%28x--6.71417707666998%29
Again, the answer is: 5.02667707666998, -6.71417707666998. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B27%2Ax%2B-540+%29