```Question 262846
Lets look at the red ball equation as
(i) {{{h(t) = -16t^2 + 96t}}}
we want to express this in vertex form to get the max ht. in vertex form the red ball is
(ii) {{{h(t) = -16(t-3)^2 + 144}}}
this tells us that (1) it is a parabola opening down; (2) after 3 seconds a max ht occurs at 144 feet.
t= 2 gives us
{{{h(2) = -16(2-3)^2 + 144}}}
{{{h(2) = 128 ft.}}}
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Lets look at the green ball equation as
(i) {{{h(t) = -16t^2 + 80t}}}
we want to express this in vertex form to get the max ht. in vertex form the green ball is
(ii) {{{h(t) = -16(t-2.5)^2 + 100}}}
this tells us that (1) it is a parabola opening down; (2) after 2.5 seconds a max ht occurs at 100 feet.
t= 2 gives us
{{{h(2) = -16(2-2.5)^2 + 100}}}
{{{h(2) = 96 ft.}}}
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Since the red ball had a great initial velocity, we have the difference formula as
D(t) = red ball equation - green ball equation
or
D(t) = -16(t-3)^2 + 144 - (-16(t-2.5)^2 + 100))
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after 2 seconds, the red ball is 32 feet higher than the green ball.
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the difference in heights will always be increasing```