SOLUTION: can you please help me with this equation??? For problems 11 through 13, a projectile is fired upward with an initial speed of 800 feet per second. It is given that {{{ h=-16t^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: can you please help me with this equation??? For problems 11 through 13, a projectile is fired upward with an initial speed of 800 feet per second. It is given that {{{ h=-16t^2      Log On


   

Question 189307: can you please help me with this equation???
For problems 11 through 13, a projectile is fired upward with an initial speed of 800 feet per second. It is given that +h=-16t%5E2%2B800t+ (h is the height of the ball).

What will you set h equal to in the equation to find how many seconds it takes for the projectile to hit the ground?
a. h = 0
b. h = 1
Found 2 solutions by Alan3354, nerdybill:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
For problems 11 through 13, a projectile is fired upward with an initial speed of 800 feet per second. It is given that (h is the height of the ball).
What will you set h equal to in the equation to find how many seconds it takes for the projectile to hit the ground?
a. h = 0
b. h = 1
---------------
h is the height. The ground is h=0, so set it to zero.

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
+h=-16t%5E2%2B800t+
.
a. h = 0
Set h to zero and solve for t:
+h=-16t%5E2%2B800t+
+0=-16t%5E2%2B800t+
+0=-16t%282t-50%29+
.
Two possible answers:
-16t = 0
t = 0 seconds (this is at the start)
.
OR
2t-50 = 0
2t = 50
t = 25 seconds (this is at the end)
.
For this problem, the solution would be 50 seconds.
.
b. h = 1
Set h to one and solve for t:
+h=-16t%5E2%2B800t+
+1=-16t%5E2%2B800t+
+0=-16t%5E2%2B800t-1+
+0=16t%5E2-800t%2B1+
Can't factor so you must resort to the quadratic equation.
Doing so will yield two solutions:
x = {49.9987 secs, 0.0013 secs}
.
Details of quadratic solution follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B-800x%2B1+=+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=%28-800%29%5E2-4%2A16%2A1=639936.

Discriminant d=639936 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--800%2B-sqrt%28+639936+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-800%29%2Bsqrt%28+639936+%29%29%2F2%5C16+=+49.9987499687484
x%5B2%5D+=+%28-%28-800%29-sqrt%28+639936+%29%29%2F2%5C16+=+0.00125003125156198

Quadratic expression 16x%5E2%2B-800x%2B1 can be factored:
16x%5E2%2B-800x%2B1+=+16%28x-49.9987499687484%29%2A%28x-0.00125003125156198%29
Again, the answer is: 49.9987499687484, 0.00125003125156198. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-800%2Ax%2B1+%29