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 secon
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-> 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 secon
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Question 320313: 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 _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?
You can put this solution on YOUR website! This same problem came up a few weeks ago, here is the response I made then
:
A red ball and a green ball are 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 being tossed is -16t^2 +80t 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 +80t)
:
Remove brackets
D(t) = -16t^2 + 96t + 16t^2 - 80t
:
combine like terms:
D(t) = 16t
:
b)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
:
c)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
