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(a) To answer this question, solve equation
h(t) = 0 = 80t - 16t^2.
The solution is t = = 5 seconds.
(b) The function H(t) = -16t^2 + 80t is a quadratic function, whose plot is a parabola opened down.
This quadratic function has the maximum at the value of its argument t = , where "a" is the coefficient at t^2
and "b" is the coefficient at t.
In your case, a= -16, b= 80, so the function gets the maximum at t = = 2.5.
So, the ball gets the maximum height 2.5 seconds after is hit straight up.
(c) To find the maximum height, calculate h(t) at t = 2.5 seconds.
= -16*2.5^2 + 80*2.5 = 100 ft.
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.
On solving similar problems to yours in this post, 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.