SOLUTION: Hi PLEASE HELP ME!! I really do NOT know what i'm doing!! I need HELP! Help would be greatly appreciated! here is the problem and directions: Use the formula h=rt-4.9t^2 where h is

Algebra ->  Equations -> SOLUTION: Hi PLEASE HELP ME!! I really do NOT know what i'm doing!! I need HELP! Help would be greatly appreciated! here is the problem and directions: Use the formula h=rt-4.9t^2 where h is      Log On


   

Question 23434: Hi PLEASE HELP ME!! I really do NOT know what i'm doing!! I need HELP! Help would be greatly appreciated! here is the problem and directions: Use the formula h=rt-4.9t^2 where h is in meters and the formula h=rt-16t^2 where h is in feet. The Problem: A ball is thrown upward with an intial speed of 24.5 m/s. when is it 19.6 m high? (Two answers)
Please help me, i'm desperate, i just cannot figure out this assignment, i'm having a lot of trouble! Thanks!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
height = -4.9t^2+(rate)t
h = -4.9t^2+24.5t
Let height be 19.6 m; what is the time?
19.6 = -4.9t^2+24.5t
-4.9t^2+24.5t-19.6=0
This is a quadratic with a=-4.9, b=24.5, c=-19.6
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.9x%5E2%2B24.5x%2B-19.6+=+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=%2824.5%29%5E2-4%2A-4.9%2A-19.6=216.09.

Discriminant d=216.09 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-24.5%2B-sqrt%28+216.09+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2824.5%29%2Bsqrt%28+216.09+%29%29%2F2%5C-4.9+=+1
x%5B2%5D+=+%28-%2824.5%29-sqrt%28+216.09+%29%29%2F2%5C-4.9+=+4

Quadratic expression -4.9x%5E2%2B24.5x%2B-19.6 can be factored:
-4.9x%5E2%2B24.5x%2B-19.6+=+-4.9%28x-1%29%2A%28x-4%29
Again, the answer is: 1, 4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B24.5%2Ax%2B-19.6+%29


So, the height is 19.6 meters after 1 second
and after 4 seconds.