Alright, so here was our task. Our group decided to pick the hippo as our fearless jumper. We were then shown where we would be bungee jumping the hippo from, which was in the stairwell of Mackinac Hall from the second floor to the first floor. We measured the distance from the top of the railing, where we would be starting, to the floor of the first floor. This gave us the distance we wanted the hippo to get as close as possible to, so that he wouldn't hit the floor. The distance we measured was 199 inches, which we converted to centimeters and got 505.46 centimeters. After, we were given 10 rubber bands and some questions to answer.
Ultimate Goal: How many rubber bands do we need to get the hippo as close to the floor, without touching, as we can?
Along with the goal came many other questions we had to answer to make an educated guess. How far does the hippo travel using one rubber band? How about two? Or three? Is the distance he travels as we add rubber bands consistent? Or does it change? How do we want to go about collecting this data? How are we going to make sure the experiment is precise? These were all running through my table mates and I's heads as we thought about how to conduct the experiment.
We attached the first rubber band securely around the back ankles of the hippo. We actually used a full rubber band just to make sure he was secure, and then attached the second rubber band, as if it was the first, so we didn't have the hippo's force on one and a half rubber bands. We held a meter stick on top of our desks, and a folder at a certain measurement to start. Sarah held the hippo with the bottom of its feet perpendicular to the top of the meter stick and we counted down, three..two..one, and she dropped him. If the hippo hit the folder we would lower it just a little, and try it again just to make sure he could travel any further. If he didn't hit the folder, we moved it up just a little to see if it could hit the folder a little higher up. When we found that the hippo was consistently reaching the same measurement at least twice, we recorded that height for the for one rubber band. We added another rubber band and did the same steps, until we found a measurement for two rubber bands. We continued this pattern to find the data shown in the table below.
|# of Rubber|
|1||27 cm||27 cm|
|2||55 cm||28 cm|
|3||75 cm||20 cm|
|4||99 cm||24 cm|
|5||117.5 cm||18.5 cm|
|7||156.5 cm||39.5 cm|
We wanted to start keeping track of the difference of the distance of a jump and the jump previous to see if there was any pattern how far the hippo traveled each time. We got to the fifth jump and found that the average between the differences so far were about 22 centimeters. For the sake of time (since we were running short on it) we knew that 7 went into 21 evenly, so we rounded our average down to 21 centimeters between jumps. We then added 2 rubber bands, at once, to see if they reached about 42 more centimeters then the measurement with 5 rubber bands. We found that the rhino traveled 156.5 centimeters, making a difference between 5 and 7 rubber bands 39.5 centimeters.
We needed to use the data we found to make a prediction about how many rubber bands we needed to use for the hippo to travel 505.46 centimeters. So, we multiplied the distance the hippo traveled with 7 rubber bands by 3, giving us 21 rubber bands. From this we found the hippo would travel about 469.5 centimeters. However, there would still be about 35.96 centimeters left for the rhino to travel to hit the ground, based on our averages we found from our data. So we decided to add another 22 centimeters, which was our average differences of the distance traveled using 7 rubber bands, to the estimated distance traveled using 21 rubber bands. This gave us a distance of 491.5 centimeters. we knew there would only be about 14 centimeters between 491.5 centimeters and 505.46 centimeters, so we decided to estimate that we would need 22 rubber bands. The work is shown in the picture below.
After we got all the rubber bands attached, we walked with the rhino to the stairwell, hoping that we made a good estimate and the hippo wouldn't "die" from hitting the floor. Here is the video of our first attempt.
We were pretty happy with only the first attempt, and I think we were about 30 centimeters from the floor, which we pretty close to what we estimated. However, It is hard to see in the video, but when Sarah released the hippo, the rubber bands got stuck on the railing a little bit and altered how much the hippo was going to travel. So, we tried one more time, and here is the second attempt close up and from a distance.
As you can see we got much closer on this try, I think the judges put us at 17 centimeters from the floor. So we predicted we would be about 14 centimeters from the floor and we were 17, which is very close to our prediction! Yay! We were happy that the way we decided to estimate worked so well.
Overall we found that in doing an experiment like this, it is very important to try to be as accurate as possible. This will hopefully give you a more accurate estimation. Also, it is more difficult to bungee jump a hippo than you think! If we were to change anything about this experiment, It would have been nice to have a way to calculate the force the hippo had using a scale and calculating the force. This would have made it easier to estimate the number of rubber bands, and it would also probably be more accurate too. Another thought is, it might have been fun to have done about 5 trials or so of the actual bungee jumping. Then we could have found an average of about how close the hippo got. I just wonder if we could have gotten him any closer. I would have also liked to try adding one more rubber band just to see if he would have hit the floor or we could have gotten him extremely close.