SOLUTION: A projectile that is fired vertically into the air with an initial velocity of 120 ft. per second can be modeled by the equation s = 120t - 16t2. In the equation, s is the distan

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Question 1168151: A projectile that is fired vertically into the air with an initial velocity of 120 ft. per second can be modeled by the equation s = 120t - 16t2. In the equation, s is the distance in feet of the projectile above the ground after t seconds.. How long will it take for a projectile to reach 216 feet? Is it possible for the projectile to reach 900 feet? Justify your answer.
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

To answer the first question, solve the quadratic equation 

    120t - 16t^2 = 216.



To answer the second question, consider the quadratic equation

    120t - 16t^2 = 900


and calculate its discriminant.



If the discriminant is non-negative real number, the answer is positive.

If the discriminant is negative real number, the answer is negative.


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In this site,  there is a bunch of lessons on a projectile thrown/shot/launched vertically up
    - Introductory lesson 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.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A projectile that is fired vertically into the air with an initial velocity of 120 ft. per second can be modeled by the equation s = 120t - 16t2.
How long will it take for a projectile to reach 216 feet?
---
120t - 16t^2 = 216
Solve for t.
2 solutions, ascending and descending.
=========================
Is it possible for the projectile to reach 900 feet?
Max height is the vertex, at t = -b/2a
t = -120/-32 seconds
Sub for t to find max height.
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