.
Looking from the Physics point of view, you simply write
t = ,
where g is the gravity acceleration (in ft/s^2), u is an initial velocity and t is the time to reach maximum height.
Substituting the data, you momentarily get
t = = 3.218 seconds.
Looking from the School Math/Algebra point of view, you write the equation for the height
h(t) = -16*t^2 + 103*t,
and from the general theory for the maximum value (vertex) of a parabola you get
t = = 3.218 seconds, i.e. the same answer.
Solved.
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On finding the maximum/minimum of a quadratic function see the lessons
- 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
in this site.
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 "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.