SOLUTION: A rocket is fired from the floor of the grand canyon. The height of the rocket, h(t) in metres above the floor of the canyon after t seconds is modeled by the function h(t)= -5t^

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rocket is fired from the floor of the grand canyon. The height of the rocket, h(t) in metres above the floor of the canyon after t seconds is modeled by the function h(t)= -5t^      Log On


   

Question 1127987: A rocket is fired from the floor of the grand canyon. The height of the rocket, h(t) in metres above the floor of the canyon after t seconds is modeled by the function h(t)= -5t^2+240t. A person sitting at the top of the canyon, 1734m above its floor, can only see the rocket when it is above that height. FOr how many seconds will the rocket be visible?
Thank you
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
You need to solve the equation


h(t) = 1734,  which is the same as  -5t^2 + 240t = 1734,   or, equivalently,


5t^2 - 240t + 1734 = 0.


Find its roots that represent the time moments when the "rocket" is at this level;

then take the difference of the roots.

That's all.

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Notice: it is a PROJECTILE, not a "rocket".

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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

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.