SOLUTION: A ball is thrown vertically upward from the ground with an initial velocity of 115ft/sec. use h=-16t^2+v0t +h0 Determine when the ball will reach its maximum height. Round to two

Algebra ->  Linear-equations -> SOLUTION: A ball is thrown vertically upward from the ground with an initial velocity of 115ft/sec. use h=-16t^2+v0t +h0 Determine when the ball will reach its maximum height. Round to two       Log On


   

Question 1104341: A ball is thrown vertically upward from the ground with an initial velocity of 115ft/sec. use h=-16t^2+v0t +h0 Determine when the ball will reach its maximum height. Round to two decimal places
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
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The formula for the height is

h(t) = -16t^2 + 115t + 0,   or simply   h(t) = -16t^2 + 115t.    (1)


The right side is a quadratic function.


The quadratic function q(x) = ax%5E2+%2B+bx+%2B+c with the negative coefficient "a" (the general form) has the maximum at x = -b%2F%282%2Aa%29.


In your case, the quadratic function (1) gets its maximum at t = -115%2F%282%2A%28-16%29%29 = 3.59 seconds.

Solved.

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To see other similar solved problems of this kind, 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

The lessons in this site on finding the maximum/minimum of a quadratic function are
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola


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 topics
"Projectiles launched/thrown and moving vertically up and dawn" and
"Finding minimum/maximum of quadratic functions".


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.