SOLUTION: 98.) 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 seco

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Question 160577: 98.) 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 feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tosses is feet.
a.) Find the polynomial D(t) that represents the difference in the height 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?

Answer by ankor@dixie-net.com(22740) (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 feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tosses is feet.
:
h = height
;
Red Ball equation:
h = -16t^2 + 96t
:
Green Ball equation
h = -16t^2 + 80t
:
a.) Find the polynomial D(t) that represents the difference in the height of the two balls.
......Red ball height - green ball height
D(t) = (-16t^2 + 96t) - (-16t^2 + 80t)
D(t) = -16t^2 + 96t + 16t^2 - 80t; removing the brackets changes the signs
D(t) = -16t^2 + 16t^2 +96t - 80t
D(t) = 16t
:
b.) How much higher is the red ball 2 seconds after the balls are tossed?
:
Replace t with 2 sec: 16(2) = 32 ft
;
c.) In reality, when does the difference in the heights stop increasing?
:
After 5 sec, Green ball hits the ground in 5 sec
You can see this:
h = -16(25) + 80(5)
h = -400 + 400
h = 0
:
:
Here's a graphical representation of the two balls