Word problem involving height difference

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diamondsmithny

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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 16t^2  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 16t^2  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?
 
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 16t^2 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 16t^2 80t feet.

a) Find a polynomial D(t) that represents the difference in
the heights of the two balls.
Click to expand...

H1 = -16t^2 + 96t
H2 = -16t^2 + 80t
D(t) = H1 – H2 = (-16t^2 + 96t) – (-16t^2 + 80t) = 96t – 80t = 16t
 
From part a, you now have a formula that calculates the difference in heights at any moment at time t.

This hint asks a couple of questions to help lead you in the right direction toward a solution for these two parts.

Part b). Intuitively, how far are they apart at time 0 (when balls are thrown into the air?) About one second later (at t=1)? Consider another second later when t=2. What do you predict? This may guide in how to use the formula. If you use the formula, would you expect the two results to match?

On part c), think about what happens in real life when something is thrown upward. Will it continue traveling upward?
When you look at the formula that models the difference in heights between the balls, are there any assumptions made that take the physics of the situation into account? (Suggestion: Graph H1, H2, and D(t) - it will help you see what's happening even more clearly.)

Hope this helps.
 
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