Question 160577
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
{{{ graph( 300, 200, -4, 8, -20, 150, -16x^2+96x, -16x^2+80x) }}}