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An astronaut on the moon throws a baseball upward. The astronaut is 6 fee, 6 inches tall and the initial velocity
of the ball is 30 feet per second. The height of the ball is approximated by the function
s(t)= -2.7t^2 + 30t + 6.5,
where t is the number of seconds after the ball was thrown.
(a) After how many seconds is the ball 12 feet above the moon’s surface?
To get the answer, solve this quadratic equation
-2.7t^2 + 30t + 6.5 = 12.
Find its two roots. They are your solutions.
(b) How many seconds after it was thrown will the ball return to the surface?
To get the answer, solve this quadratic equation
-2.7t^2 + 30t + 6.5 = 0.
Find its two roots. The positive root will be your solutions.
(c) The ball will never reach a height of 100 feet. How can this be determined analytically?
Find the vertex of the given quadratic function.
It will give you the maximum value of the function, which is the maximum height.
On how to do it, 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.