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Question 181660: A red ball and a green ball are
simultaneously tossed into the air. The red ball is given an
initial velocity of 96 feet per second, and its height t seconds
after it is tossed is _16t2 _ 96t feet. The green ball
is given an initial velocity of 80 feet per second, and its
height t seconds after it is tossed is _16t2 _ 80t feet.
a) Find a polynomial D(t) that represents the difference in
the heights of the two balls.
b) How much higher is the red ball 2 seconds after the
balls are tossed?
c) In reality, when does the difference in the heights stop increasing?
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A red ball and a green ball are
simultaneously tossed into the air. The red ball is given an
initial velocity of 96 feet per second, and its height t seconds
after it is tossed is _16t2 _ 96t feet. The green ball
is given an initial velocity of 80 feet per second, and its
height t seconds after it is tossed is _16t2 _ 80t feet.
a) Find a polynomial D(t) that represents the difference in
the heights of the two balls.
b) How much higher is the red ball 2 seconds after the
balls are tossed?
c) In reality, when does the difference in the heights stop increasing?
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It's -16t^2 + 96t, and
-16t^2 + 80t
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a) Find a polynomial D(t) that represents the difference in
the heights of the two balls.
The difference in height is the difference between the 2 equations, which is
16t
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b) How much higher is the red ball 2 seconds after the
balls are tossed?
Red: h = -16*4 + 192 = 128 feet
Grn: h = -16*4 + 160 = 96 feet
The difference is 32 feet, which is 16t.
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c) In reality, when does the difference in the heights stop increasing?
The difference increases at a rate of 16t feet/second until the first ball (the green one) hits the ground at t=5.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! A red ball and a green ball are simultaneously tossed into the air.
The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16t2 + 96t feet.
The green ball is given an initial velocity of 80 feet per second, and its
height t seconds after it is tossed is -16t2 + 80t feet.
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a) Find a polynomial D(t) that represents the difference in
the heights of the two balls.
D(t) = red - blue = 16t
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b) How much higher is the red ball 2 seconds after the
balls are tossed?
D(2) = 16*2 = 32 ft.
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c) In reality, when does the difference in the heights stop increasing?
When the height of the blue ball reaches zero.
h(t) = -16t^2 + 80t = 0
-16t(t-5) = 0
t = 5 seconds
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Cheers,
Stan H.
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