SOLUTION: he path of a model rocket is modelled by the quadratic function h(t)=-5(t-20^+ 25, where the height, h(t),is in meters and time,t,is in seconds. a) when will the rocket reach a he

Question 1166719: he path of a model rocket is modelled by the quadratic function h(t)=-5(t-20^+ 25, where the height, h(t),is in meters and time,t,is in seconds.
a) when will the rocket reach a height of 20 meters?
b)was the rocket in their after 4 seconds?
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.

The formula in your post is written incorrectly.

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.

---------------

If you have the 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.




    (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).

What's all you need to know.

To answer your questions, use my instructions and make calculations on your own.

---------------

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.

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