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. r = 0.8h + 0.2
B. r = 0.8h - 0.2
C. r = 0.8h
D. r = 0.2h
C. r = 0.8h
explain it
To determine the equation that represents the proportional relationship between the initial height (h) and the rebound height (r) of the bouncy ball, we can analyze the given data.
Looking at the data, we can see that the rebound height is always 0.8 times the initial height.
For example, when the initial height is 0.30 meters, the rebound height is 0.24 meters, which is 0.8 times the initial height.
This relationship holds true for all the other values as well.
Therefore, the equation that represents the proportional relationship between the initial height and the rebound height is r = 0.8h.
To determine the equation that represents the proportional relationship between the initial height (h) and the rebound height (r) of the bouncy ball, we need to examine the given data and look for a consistent pattern.
We can start by analyzing the ratio between the rebound height and the initial height for each data point. If the relationship is proportional, these ratios should be constant.
Let's calculate the ratios:
For h = 0.30, r = 0.24 → r/h = 0.24/0.30 = 0.8
For h = 0.50, r = 0.40 → r/h = 0.40/0.50 = 0.8
For h = 0.80, r = 0.64 → r/h = 0.64/0.80 = 0.8
For h = 1.00, r = 0.80 → r/h = 0.80/1.00 = 0.8
For h = 1.20, r = 0.96 → r/h = 0.96/1.20 = 0.8
We observe that the ratio r/h is constant at 0.8 for all the data points. This constant ratio indicates a proportional relationship.
Now, let's look at the equation choices:
A. r = 0.8h + 0.2
B. r = 0.8h - 0.2
C. r = 0.8h
D. r = 0.2h
Comparing the constant ratio we calculated (0.8) with the equation choices, we see that option C, r = 0.8h, represents the proportional relationship between the initial height and the rebound height of the bouncy ball.
Therefore, the correct answer is C. r = 0.8h.