SOLUTION: 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
Algebra.Com
Question 191725This question is from textbook Elementary and Intermediate Algebra
: 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?
This question is from textbook Elementary and Intermediate Algebra
Answer by ankor@dixie-net.com(22740) (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.
;
-16t^2 + 96t = h (redball)
and
-16t^2 + 80t = h (greenball)
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
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 after 2 sec
:
c) In reality, when does the difference in the heights stop
increasing?
When the green ball hits the ground. h = 0
If you solve -16t^2 + 80t = 0, you will find that will occur in 5 sec
;
Seen graphically; x axis is time in seconds, y axis is height in feet
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