.
The height s of a ball after t seconds when thrown straight up with an initial speed of 70 feet per second from
an initial height of 5 feet can be modeled by the function s(t)= -16t^2+70t+5.
(a) When will the height of the ball be 40 feet?
When -16t^2+70t+5 = 40.
Solve the quadratic equation and find t.
(b) When will the height of the ball be at 60 feet?
When -16t^2+70t+5 = 60.
Solve the quadratic equation and find t.
(c) Will the ball ever reach a height of 150 feet?
The ball will get the maximum height at t= = = 2.1875 seconds and the maximum height will be
h(2.1875) = -16*2.1875^2 + 70*2.1875 + 5 = 81.5625 feet.
--------------
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.
On a projectile thrown/shot/launched vertically up, see 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.
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
"Finding minimum/maximum of quadratic functions" and
"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.