SOLUTION: I do not know where to start.
A red ball and a green ball are simultaneously tossed into the air.
Find a polynomial D(t) that represents the difference in the heights of the two
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Question 262846: I do not know where to start.
A red ball and a green ball are simultaneously tossed into the air.
Find a polynomial D(t) that represents the difference in the heights of the two balls. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16t^2 + 96t feet. The green ball is given an initial velocity of 80feet per second, and its height t second, and its height t seconds after it is tossed is -16t^ + 80t feet. How much higher is the red ball 2 seconds after the balls are tossed? In reality, when does the difference in the heights stop increasing?
Found 2 solutions by ankor@dixie-net.com, drk:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find a polynomial D(t) that represents the difference in the heights of the two balls.
The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16t^2 + 96t feet.
The green ball is given an initial velocity of 80feet per second, and its height t second, and its height t seconds after it is tossed is -16t^ + 80t feet.
How much higher is the red ball 2 seconds after the balls are tossed?
In reality, when does the difference in the heights stop increasing?
:
D(t) = (-16t^2 + 96t) - (-16t^2 +80t)
:
Remove brackets
D(t) = -16t^2 + 96t + 16t^2 - 80t
:
combine like terms:
D(t) = 16t
:
How much higher is the red ball 2 seconds after the balls are tossed?
D(t) = 16(2)
D(t) = 32 ft difference after 2 seconds
:
When does the difference in the heights stop increasing?
:
Obviously, when one of the balls hits the ground
:
Find when the lowest ball hits the ground (h=0)
-16t^2 + 80t = 0
Factor out -16t
-16t(t - 5) = 0
t = 5 seconds when the difference stops increasing;
:
A graph illustrates this well
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Lets look at the red ball equation as
(i)
we want to express this in vertex form to get the max ht. in vertex form the red ball is
(ii)
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
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Lets look at the green ball equation as
(i)
we want to express this in vertex form to get the max ht. in vertex form the green ball is
(ii)
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
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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