SOLUTION: A diver jumps from a 48 foot cliff into the ocean below with an initial velocity of 8 ft/sec. The height of the diver from the ocean after t sec is given by h = -16t2 + 8t + 48. Wh

Algebra ->  Expressions-with-variables -> SOLUTION: A diver jumps from a 48 foot cliff into the ocean below with an initial velocity of 8 ft/sec. The height of the diver from the ocean after t sec is given by h = -16t2 + 8t + 48. Wh      Log On


   

Question 300908: A diver jumps from a 48 foot cliff into the ocean below with an initial velocity of 8 ft/sec. The height of the diver from the ocean after t sec is given by h = -16t2 + 8t + 48. When does the diver hit the water?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h = -16t2 + 8t + 48. When does the diver hit the water?
------------
When h = 0
-16t^2 + 8t + 48 = 0
Solve for t
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B1x%2B6+=+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=%281%29%5E2-4%2A-2%2A6=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+49+%29%29%2F2%5C-2+=+-1.5
x%5B2%5D+=+%28-%281%29-sqrt%28+49+%29%29%2F2%5C-2+=+2

Quadratic expression -2x%5E2%2B1x%2B6 can be factored:
-2x%5E2%2B1x%2B6+=+%28x--1.5%29%2A%28x-2%29
Again, the answer is: -1.5, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B1%2Ax%2B6+%29


--------------------
t = 2 seconds