SOLUTION: a toy rocket is launched from a 2.1 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h= -4.9t^2 + 14.0t + 2.1. How long will i

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: a toy rocket is launched from a 2.1 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h= -4.9t^2 + 14.0t + 2.1. How long will i      Log On


   

Question 344463: a toy rocket is launched from a 2.1 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h= -4.9t^2 + 14.0t + 2.1. How long will it take for the rocket to hit the ground?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Set h to zero and solve for t:
h= -4.9t^2 + 14.0t + 2.1
0= -4.9t^2 + 14.0t + 2.1
Apply quadratic formula to get:
t = {-0.143, 3}
You can toss out the negative solution leaving:
t = 3 seconds
.
Details of quadratic to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -4.9t%5E2%2B14t%2B2.1+=+0) has the following solutons:

t%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=%2814%29%5E2-4%2A-4.9%2A2.1=237.16.

Discriminant d=237.16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-14%2B-sqrt%28+237.16+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2814%29%2Bsqrt%28+237.16+%29%29%2F2%5C-4.9+=+-0.142857142857143
t%5B2%5D+=+%28-%2814%29-sqrt%28+237.16+%29%29%2F2%5C-4.9+=+3

Quadratic expression -4.9t%5E2%2B14t%2B2.1 can be factored:
-4.9t%5E2%2B14t%2B2.1+=+-4.9%28t--0.142857142857143%29%2A%28t-3%29
Again, the answer is: -0.142857142857143, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B14%2Ax%2B2.1+%29