SOLUTION: Height difference. 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

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Question 206329: Height difference. 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 - 16t^2 + 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 - 16t^2 + 80 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?
I am not even sure how to find any of these solutions and am not even sure how to set up the problems to solve them. Please share the formulas using applications so I may solve.
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Height difference. 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 - 16t^2 + 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 - 16t^2 + 80 feet.
a) Find a polynomial D(t) that represents the difference in the heights of the two balls?
D(t) = -16t^2+96t -(-16t^2+80) = 96t-80
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b) How much higher is the red ball 2 seconds after the balls are tossed?
D(2) = 96*2-80 = 192-80 = 112 feet
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c) In reality, when does the difference in the heights stop increasing?
When the difference is zero:
96t-80 = 0
t = 80/96 = 0.83 seconds
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I am not even sure how to find any of these solutions and am not even sure how to set up the problems to solve them. Please share the formulas using applications so I may solve.
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Cheers,
Stan H.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you are given the expressions you need for a solution (there should be a t with the 80 in the second expression)

a) the difference in heights is the difference (subtraction) in the two expressions
___ D(t) = (- 16t^2 + 96t) - (- 16t^2 + 80t) = 16t

b) using D(t) ___ D(2) = 16(2) = 32

c) the height difference will increase as long as both balls are in freefall
___ this stops when the lower (green) ball hits the ground