.
At time t=0, a ball was thrown upward from an initial height of 4 feet.
The ball's height, in feet, after t seconds is given by the function h above,
in which both c and d are positive constants. If the ball reached its maximum height
of 104 feet at time t=3, what is the height, in feet, of the ball at time t=1.5?
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In this problem, the standard quadratic function of height, h(t) = -16t^2 + ut + h0, is presented
in vertex form, and your first task is to identify the parameters of this vertex form.
I will help you to identify these parameters.
First, the term "c" represents the highest position of the ball, which is given in the problem as 104 feet.
So, c = 104 feet.
Second, d - 4t = 0 determines the time "t", when the highest position is reached.
The problem says that the maximum height is reached at t= 3 seconds; hence, d= 4t = 4*3 = 12 seconds.
Now you know everything about your function: it is h(t) = 104 - (12-4t)^2.
Now to answer the problem's question, you simply substitute t= 1.5 seconds in the last formula.
You get then
h(1.5) = 104 - (12 - 4*1.5)^2 = 68 feet. ANSWER
Thus, the solution of this tangled problem is completed.
Solved, explained and completed.
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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 on 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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Post-solution notes at the end:
(a) the initial condition "at time t=0, a ball was thrown upward from an initial height of 4 feet"
is not used in the solution. So, this condition is EXCESSIVE and UNNECESSARY.
By the way, this condition is INCONSISTENT with the rest of the problem,
so IT MUST BE EXCLUDED from the problem, for clarity.
(b) To solve the problem, it is assumed that the reader/(the student) firmly knows the prerequisites
that are given in the lessons listed in my post.
This knowledge is a NECESSARY condition to solve the problem.
If you know these prerequisites, you are able to solve the problem and to understand the solution.
If you do not know them, you will find yourselves in difficult position.