As part of a science experiment, Natasha drops a bouncy ball from various heights, h, and observes the height to which the ball rebounds, r. The table shows the results of Natasha's experiment.
Initial height, h (in meters) Rebound height, r (in meters)
0.30 0.24
0.50 0.4
0.80 0.64
1.00 0.8
1.20 0.96
Which equation represents the proportional relationship between the initial height and the rebound height of the bouncy ball?
A.
B.
C.
D.
C. r = 0.8h
explain
To determine the equation representing the proportional relationship between the initial height (h) and the rebound height (r) of the bouncy ball, we need to look for a constant ratio between the two variables.
The constant ratio can be found by dividing the rebound height (r) by the initial height (h) for each corresponding data pair.
For example, when h = 0.30, r = 0.24. The ratio is r/h = 0.24/0.30 = 0.8.
If we calculate the ratio for all the data pairs, we get the following values:
h = 0.30, r = 0.24, r/h = 0.8
h = 0.50, r = 0.40, r/h = 0.8
h = 0.80, r = 0.64, r/h = 0.8
h = 1.00, r = 0.80, r/h = 0.8
h = 1.20, r = 0.96, r/h = 0.8
As we can see, the ratio r/h is constant for all the data pairs, equal to 0.8.
Therefore, the equation representing the proportional relationship between the initial height (h) and the rebound height (r) of the bouncy ball is r = 0.8h. This is option C.
but that's answer choice A
You are correct. I apologize for the confusion. Option A, r = 0.8h, represents the proportional relationship between the initial height and the rebound height of the bouncy ball. This equation shows that the rebound height (r) is equal to 0.8 times the initial height (h), indicating a constant ratio between the two variables.
To find the equation that represents the proportional relationship between the initial height (h) and the rebound height (r) of the bouncy ball, we need to determine the constant of proportionality.
The constant of proportionality represents the ratio between the initial height and the rebound height. We can calculate this ratio by dividing the rebound height by the initial height for each set of data.
Let's do the calculations:
For the first set of data, h = 0.30 and r = 0.24, the ratio r/h = 0.24/0.30 = 0.8.
For the second set of data, h = 0.50 and r = 0.40, the ratio r/h = 0.40/0.50 = 0.8.
For the third set of data, h = 0.80 and r = 0.64, the ratio r/h = 0.64/0.80 = 0.8.
For the fourth set of data, h = 1.00 and r = 0.80, the ratio r/h = 0.80/1.00 = 0.8.
For the fifth set of data, h = 1.20 and r = 0.96, the ratio r/h = 0.96/1.20 = 0.8.
From the calculations, we can see that the ratio r/h is always equal to 0.8. This means that the rebound height is always 0.8 times the initial height. Therefore, the proportional relationship between the initial height and the rebound height can be represented by the equation:
r = 0.8h
The correct answer is:
B. r = 0.8h