BOREDOM'S
DEMISE
TIRED OF ROAMING THROUGH
STORES WAITING FOR LOVED ONES WHO NEVER SEEM TO GET
TIRED OF SHOPPING?
Try Having Escalator Fun!!!
Escalator fun is an exciting experiment that
originated from a college math class called Survey of
College Math.
You can use it to keep yourself busy while you wait on
that
SHOPPER FROM THE BLACK LAGOON.
Here's what you need to do:
First, you need a tape measure and a stopwatch.
Second, use a string, maybe a ball of yarn, to
measure the escalator's height from the point of
exiting the escalator
to the floor below. Then, cut the string and
measure it by using the tape measure; simply lay the
string along side the tape measure.
Third, use the tape measure to find the length
of the escalator. This is better off done on the floor
beside the front entrance to the escalator, but start
the tape measure at the point that the escalator
begins to rise to the point at which the escalator
steps flatten.
Fourth, get on the escalator with the stopwatch
clear and ready so that you can start the watch at the
point that the escalator rises and stop the watch at
the point the escalator steps flatten.
Now you're ready to find the length of the escalator
by using a formula called Pythagorean theorem ((a)
Squared + (b) squared = (c) squared)
This formula is a crucial part of this experiment and
in order to give
you an idea of why this formula is an important part
of this experiment
I will now use measurements from the original
experiment called
Escalator Fun At St. Louis Galleria.
It's the same thing you're doing which
is an experiment that originated from the Survey of
College math class.
Okay, now that you know the history of what you're
doing here are the measurements that derived from the
original experiment:
In the original experiment it was 29 feet 3 inches
from the entrance of the
escalator to the exit or point at which the escalator
steps flatten and 208
inches from the flattening point of the
escalator steps to the ground floor.
First, turn the feet to inches in order to simplify
the results by multiplying 29 feet by 12 because there
are 12 inches in a foot. Now you have 348
inches. Add the 3 inches, plus 12 more, and get 363
inches from entrance to post.
Second, Now put 363 inches and 208 inches into the
Pythagorean Theorem ((a) squared + (b) squared = (c)
squared)
Now it looks like this: 363 squared + 208 squared = c
squared
19.05255888 + 208 squared = c squared
19.05255888 + 14.4222051 = c squared
19.05255888 + 14.4222051 = 33.47476398 squared
19.05255888 + 14.4222051 = 5.785737981 inches
X= 5.785737981
This class experiment was performed six times but
we're just going to use the average seconds it took
from the rise and fall of the
escalator steps, which was 22.5415 seconds.
Now, lets calculate how long it took to do the
experiment using the Distance
Formula (D=rt or distance, rate, and time)
First, plug the numbers into the formula as such:
5.785737981 is distance and 22.5415 is time
5.785737981 inches = r x 22.5415 seconds
Next, divide both sides by the number of seconds now
the formula looks like this:
5.785737981 inches/22.5415 seconds = r
22.5415/22.5415
Now, the numbers on the right side cancel out leaving
you with r by it self as such:
5.785737981/22.5415 = r
divide the number to find out the rate in inches per
second and you get:
0.256670495 = r, or r = 0.256670495 inches/second
If you would like to see this in miles per hour,
convert the measurements of the escalator to feet and
use the same average seconds.
First, turn the inches to feet in order to simplify
the results, so add 3 inches to 29 feet by dividing 3
inches by
12 in order to get a decimal number. Now you have
29.25 feet
from entrance to post.
Second, convert 208 inches to feet by dividing 208
inches by 12 in order to
find out how many feet are in 208 inches. There are
17.33 feet from the point
at which the escalator steps flattens to the ground
floor.
Third plug the numbers into the Pythagorean theorem
((a) squared + (b) squared = (c)
squared)
Now it looks like this: 29.25ft squared + 17.33ft
squared = c
squared
29.25 ft squared + 17.33 ft squared = c squared
5.408326913 ft + 4.162931659 ft = c squared
5.408326913 ft + 4.162931659 ft= 9.571258573 squared
5.408326913 ft + 4.162931659 ft = 3.093745072 ft
X= 3.093745072 feet
In order to convert to miles per/hour divide 5,280
by 3.093745072 feet miles since there are 5280 feet in
a mile.
This gives you 1706.669385 miles. To convert seconds
to hours divide
22.5415 seconds by 60 since there are 60 minutes in an
hour.
This gives you 2.661757203 hours.
Now, lets calculate the how long it took to do the
experiments using the Distance
Formula (D=rt or distance, rate, and time)
First, plug the numbers into the formula as such:
1706.669385 miles is distance and 2.661757203 hours is
time
1706.669385 miles = r x 2.661757203 hours
Next, divide both sides by the number of hours now
the formula looks like this:
1706.669385 miles/2.661757203 hours = r x 2.661757203
hours/2.661757203 hours
Now, the numbers on the right side cancel out leaving
you with r by it self as such:
1706.669385 miles/2.661757203 hours = r
divide the number to find out the rate in miles per
hour and you get:
641.1814658 = r, or r = 641.1814658 miles per/hour
Okay, now your equipped for your next shopping trip
with the
SHOPPER FROM THE BLACK LAGOON.
In combing the results of "Out juggling In My Survey
Of College Math Class" and
"Walkway Fun At Lambert Airport," I found out that if
I walked on the moving walkway
I would be going 7.425 feet/second; since, I walked
5.4 ft/second and the walkway moved
at 2.025 ft/second.
color=green face=jester>[ d = r t
]
Related Concepts:
Speed
Function Notation
Y Rate
X
Rate
Slope
Linear
Functions
Related
Rate Equations
Linear
Motion
History of d
= r t
Notes And Hints:
For more information and ideas about this project you may link to a page
written by one of the following math artists:
Danielle,
Darlene,
Kellie,
Jill,
Nanyal's Second and Fourth Web Page,
Kevin,
Crystal,
Rachel,
Christina,
Jennifer,
Candice,
Vincent,
Esther and
Melinda.
Most of us are in this picture but not in order of names.
