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 ->
Polynomials-and-rational-expressions
-> 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
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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
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
