SOLUTION: I would really just appreciate if someone can guide me an the formulas to use. This is credit, and we havent done this chapter. Much appreciated... A miniature rocket is launc

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: I would really just appreciate if someone can guide me an the formulas to use. This is credit, and we havent done this chapter. Much appreciated... A miniature rocket is launc      Log On


   

Question 277224: I would really just appreciate if someone can guide me an the formulas to use. This is credit, and we havent done this chapter. Much appreciated...
A miniature rocket is launched so that its height h in meters after t seconds is given by the equation h = -4.9t^2 + 19.6t + 10
a. draw a graph of the equation
b. how high is it after 3 sec?
c. what is the max height the rocket will attain?
d. How long after the launch will the rocket hit the ground?
Found 2 solutions by Monarita, Alan3354:
Answer by Monarita(1) About Me  (Show Source):
You can put this solution on YOUR website!
Still me...
B) I got 24.7
c) 29.6 meter
D) 10 seconds??

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A miniature rocket is launched so that its height h in meters after t seconds is given by the equation h = -4.9t^2 + 19.6t + 10
a. draw a graph of the equation
b. how high is it after 3 sec?
Sub 3 for t
h(3) = -4.9*9 + 19.6*3 + 10
= 24.7 meters
----------------------
c. what is the max height the rocket will attain?
Max height is at the vertex, t = -b/2a
t = -19.6/2*-4.9 = 2 seconds
h(2) = -19.6 + 39.2 + 10
h(2) = 29.6 meters max height
-------------------------------
d. How long after the launch will the rocket hit the ground?
It impacts at h = 0
-4.9t^2 + 19.6t + 10
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.9x%5E2%2B19.6x%2B10+=+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=%2819.6%29%5E2-4%2A-4.9%2A10=580.16.

Discriminant d=580.16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-19.6%2B-sqrt%28+580.16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2819.6%29%2Bsqrt%28+580.16+%29%29%2F2%5C-4.9+=+-0.457807219155036
x%5B2%5D+=+%28-%2819.6%29-sqrt%28+580.16+%29%29%2F2%5C-4.9+=+4.45780721915504

Quadratic expression -4.9x%5E2%2B19.6x%2B10 can be factored:
-4.9x%5E2%2B19.6x%2B10+=+%28x--0.457807219155036%29%2A%28x-4.45780721915504%29
Again, the answer is: -0.457807219155036, 4.45780721915504. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B19.6%2Ax%2B10+%29

---------------------
t = x