.
A ball is thrown off the top of building. At time t (in seconds), its height
(in feet) follows the the path s(t)=-3t^2 + 24t + 60?
At what time does the ball reach its maximum height?
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As it is written, this formula does not work.
Introduction written specially for beginners who don't know the subject AT ALL
The formula in your post is written incorrectly. FATALLY INCORRECTLY, it is what I want to say.
I observed it many times in this forum that the students / (the visitors) write this formula incorrectly.
because they do not understand the meaning of its terms.
So I prepared this text below as a standard introduction to the subject for such students / visitors.
Be calm, you are in good hands, and read my post to the very end.
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If you have the formula for a height given to you as a function of time in the form
h(t) = -at^2 + bt + c, (1)
where "a", "b" and "c" are real numbers, a > 0, then in this formula
(a) the initial height is equal to the coefficient "c" value;
(b) the initial velocity is the coefficient "b" in the formula;
(c) the coefficient "a" value is half of the gravity acceleration.
For the Earth conditions, the gravity acceleration is g = 9.8 m/s^2, or 32 ft/s^2.
THEREFORE, if you use feet for height, you should use the approximate value of g = 32 ft/s^2.
So, in this case a = = 16 (the numerical value).
ALTERNATIVELY, if you use meters for height, you should use the approximate value of g = 9.8 ft/s^2.
So, in this case a = = 4.9 (the numerical value).
(d) To find the height at the time moment "t", simply substitute the value of "t" into the formula (1) and calculate.
(e) To find the time "t" when the height has a given value h = , substitute h = into equation (1)
and solve equation
h(t) = -at^2 + bt + c = . (2)
(f) To find the time when the height is maximal, use the formula
= . (3)
(g) To find the maximal height, substitute the time value t= of the formula (3) into the formula (1).
That's all you need to know.
After my explanations, you can solve the problem on YOUR OWN now,
but for it, you should have your governing equation written correctly.
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To see numerous examples of solved problems, look into the lessons
- 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
in this site.
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.
================
If this introduction is helpful to you, I will be happy.
If it is not enough for you to solve the problem, come again,
but with one indispensable condition: your equation MUST be written correctly (showing your understanding).
Come again, if you need.
\\\\\\\\\\\\\ ATTENTION ( ! ) ATTENTION ( ! ) ATTENTION ( ! ) //////////////
What this lady @ewatrrr calculated for you, is INCORRECT, since she wrote and used wrong coefficient in the equation.
I expected from YOU, the visitor, that YOU (and not somebody else instead of you), will post
to the forum the correct equation, after my explanations.
If you do not make it, then I CAN NOT be responsible for correctness of calculations, that @ewatrrr makes for you -
- she simply does not know the subject and does not give a labor to herself to read my posts attentively.
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I can not control what she makes at this forum, at all,
as well as can not control her activity.
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To tutor @math_tutor2020 and to all other tutors:
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The way on how I do it,
is the only way to teach RIGHT.
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