SOLUTION: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. A water rocket is launched upward with an initial velocity of 48 ft/sec. I

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. A water rocket is launched upward with an initial velocity of 48 ft/sec. I      Log On


   

Question 302185: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
A water rocket is launched upward with an initial velocity of 48 ft/sec. Its height h, in feet, after t seconds is given by h = 48t - 16t2. After how many seconds will the height of the rocket be 20 feet? Show work
can some one please helpme with this
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h = 48t - 16t2
Set h = 20 and solve for t
20 = 48t - 16t2
-16t^2 + 48t - 20 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B48x%2B-20+=+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=%2848%29%5E2-4%2A-16%2A-20=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-48%2B-sqrt%28+1024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2848%29%2Bsqrt%28+1024+%29%29%2F2%5C-16+=+0.5
x%5B2%5D+=+%28-%2848%29-sqrt%28+1024+%29%29%2F2%5C-16+=+2.5

Quadratic expression -16x%5E2%2B48x%2B-20 can be factored:
-16x%5E2%2B48x%2B-20+=+%28x-0.5%29%2A%28x-2.5%29
Again, the answer is: 0.5, 2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B48%2Ax%2B-20+%29


t = x-axis, h = y-axis
It's a 20 ft going up, then again coming down.