SOLUTION: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)= −4.9t2 squared + 325t + 353. Assuming that the rocket

Algebra ->  Rectangles -> SOLUTION: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)= −4.9t2 squared + 325t + 353. Assuming that the rocket      Log On


   

Question 1187268: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)= −4.9t2 squared + 325t + 353.


Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? For intermediate work, keep at least five decimal places. For the final answer, round to the nearest hundredth.

The rocket splashes down after seconds.

How high above sea-level does the rocket get at its peak?


The rocket peaks at meters above sea-level.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)= −4.9t2 squared + 325t + 353.
==========================
Rockets launched by NASA have thrust.
That's a projectile.

Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
It's when h(t) = 0
h(t)= −4.9t^2 + 325t + 353 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.9x%5E2%2B325x%2B353+=+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=%28325%29%5E2-4%2A-4.9%2A353=112543.8.

Discriminant d=112543.8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-325%2B-sqrt%28+112543.8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28325%29%2Bsqrt%28+112543.8+%29%29%2F2%5C-4.9+=+-1.06892688325969
x%5B2%5D+=+%28-%28325%29-sqrt%28+112543.8+%29%29%2F2%5C-4.9+=+67.3954574955046

Quadratic expression -4.9x%5E2%2B325x%2B353 can be factored:
-4.9x%5E2%2B325x%2B353+=+%28x--1.06892688325969%29%2A%28x-67.3954574955046%29
Again, the answer is: -1.06892688325969, 67.3954574955046. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B325%2Ax%2B353+%29

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t = 67.395 seconds
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Do NOT include this
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The rocket splashes down after seconds.
How high above sea-level does the rocket get at its peak?

The rocket peaks at meters above sea-level.

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

In this site,  there is a bunch of lessons on a projectile thrown/shot/launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform

Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.
Read them attentively and learn how to solve this type of problems once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.