SOLUTION: I am having problems with this question, please could you help me to understand it? I open a bottle of champagne and release the cork vertically from the bottle. The height in

Question 204830: I am having problems with this question, please could you help me to understand it?
I open a bottle of champagne and release the cork vertically from the bottle. The height in metres of the cork above the level of the ground at time (t) seconds is modelled by the equation
h = 1 + 8t - 5t^2.
a) find the height of the cork after 0.8s....i have the answer of 4.2m for this.
b) find the time when the cork is at ground level (h = 0)......i have the answer of 1.72s for this.
c) explain what the maximum value of t is for which this function is a plausible model for the height of the cork?....i don't understand this question.
hope you can help me by explaining how to do this

thank you
Dawn

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
h = 1 + 8t - 5t^2.
a) find the height of the cork after 0.8s....i have the answer of 4.2m for this.
Correct.
b) find the time when the cork is at ground level (h = 0)......i have the answer of 1.72s for this.
Correct.
c) explain what the maximum value of t is for which this function is a plausible model for the height of the cork?....i don't understand this question.
hope you can help me by explaining how to do this
.
By inspection of:
h = 1 + 8t - 5t^2
Rewritten as:
h = -5t^2 + 8t + 1
.
We see that is is a parabola and it opens downward (upside down U). We can tell by looking at the coefficient associated with the t^2 term (-5) -- since it is negative, think "sad face". Because of this, we now know that the VERTEX of the parabola is your maximum height/time pair.
There are several ways to find this vertex.
One way is to find the "axis of symmetry"
t = -b/2a = -8/(2(-5)) = -8/(-10) = 8/10 = 4/5 = .8 seconds
.
Height, at that time is:
h = -5t^2 + 8t + 1
h = -5(.8)^2 + 8(.8) + 1
h = 4.2m
Which is "part a" of this problem.

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