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Bouncing Ball Question

Lee Way was conducting an experiment with a new mega ball. Use the following tables of values to complete the question for Part I
(A) Identify the independent variable and the dependent variable.
x=_________________ y=_____________

(B) Graph your results

(C) What is the rebounding height if the ball is dropped from 10 feet

(D) If the ball was dropped from n feet, how high would it bounce?

(E) Is this graph discrete or continuous? Support your conclusion using words, graph, and or diagram.

Part 2: Lee Way wanted to know how long his megaball will bounce. Use the information from Part I, complete the following question:

(A) What is the rebound ratio of the megaball. (hint:rebound ratio=rebound height/starting height).

(B) What is the height of the ball after the 5th bounce if the ball is dropped from 10 feet?

(C) What is the height of the ball after the nth bounce?

(D) Starting at 10 feet height make the table and draw a graph of the predicted rebound height for each bounce on based on the rebound ratio that you calculated in (A).

(E) Should the points on your graph be connected?

(F) Is this graph discrete or continuous? Support your conclusion using words, graphs, and or diagram.

See attached file for full problem description.

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Solution This solution is FREE courtesy of BrainMass!

Lee Way was conducting an experiment with a new mega ball. Use the following tables of values to complete the question for Part I
(A) Identify the independent variable and the dependent variable.
x=_________________ y=_____________

The starting height is the x variable (independent) because that is what you control. The rebound height is the y variable (dependent) because that is dependent on the starting height.

(B) Graph your results

I graphed them in Excel.

The points are not perfectly linear, but they are very close.

(C) What is the rebounding height if the ball is dropped from 10 feet

Ten feet is the same as 120 in. The graph doesn't show that point, but we can guess based on the results we have.

If we look at the numbers we get by dividing the rebound height by the starting height, we get the following results:
Starting Height 70 60 50 40 30 20 10
Rebound Height 40 34 29 23 17 11 6

Rebound/Starting 0.571429 0.566667 0.58 0.575 0.566667 0.55 0.6

When you divide the rebound height by the starting height, you get a number around 0.55 to 0.60. The average of these numbers is 0.5728. We can use that to estimate the rebound height for a starting height of 120 inches:

120*0.5728 = 68.74 inches.

The rebound height would be 68.74 inches (or 5.728 feet).

(D) If the ball was dropped from n feet, how high would it bounce?

Using the same estimation of the ratio of the rebound height to starting height, the rebound height would be 0.5728n feet.

(E) Is this graph discrete or continuous? Support your conclusion using words, graph, and or diagram.

This graph is continuous. If you connected the points in the graph above with a line, the line would provide a good estimation of the rebound height for x values other than the ones we already graphed. The graph would be valid for any x you chose.

If you looked at two values of x, the closer they were to each other, the closer their corresponding y-values would be. This makes the graph continuous.

Part 2: Lee Way wanted to know how long his megaball will bounce. Use the information from Part I, complete the following question:

(A) What is the rebound ratio of the megaball. (hint:rebound ratio=rebound height/starting height).

As we showed above, the rebound ratio is 0.5728.

(B) What is the height of the ball after the 5th bounce if the ball is dropped from 10 feet?

Let's make a table to look at the height after each bounce. The rebound height after each bounce will be equal to the height of the previous bounce multiplied by 0.5728.

bounce # rebound height after that bounce
0 10 feet (starting height)
1 10*0.5728 = 5.728
2 10*0.5728*0.5728 = 3.281
3 10*0.5728*0.5728*0.5728 = 1.879
4 10*0.5728*0.5728*0.5728*0.5728 = 1.076
5 10*0.5728*0.5728*0.5728*0.5728*0.5728 = 0.617

After the 5th bounce, the rebound height is 0.617 feet, or 7.399 inches.

(C) What is the height of the ball after the nth bounce?

Look at the rebound heights in the table above. After the 3rd bounce, the rebound height is 10(0.5728)3; after the 4th bounce, the rebound height is 10(0.5728)4, etc. If you follow that pattern, then after the nth bounce, the rebound height is 10(0.5728)n.

(D) Starting at 10 feet height make the table and draw a graph of the predicted rebound height for each bounce on based on the rebound ratio that you calculated in (A).

The table was made in part b.

(E) Should the points on your graph be connected?
(F) Is this graph discrete or continuous? Support your conclusion using words, graphs, and or diagram.

You should not connect the points on the graph because this graph is discrete, not continuous. This is because you can't graph a value for any x-value in between the values we already have in the graph (for example, there is no such thing as the one-and-a-halfth bounce, so you couldn't graph a point in between bounce numbers 1 and 2). If you connect the points in the graph, this suggests that there can be data points in between the points that are on the graph now. Compare this to the data from part I.

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