Due Friday, Apr 28, 2000, at the beginning of class
Your job this week is to use three different techniques to climb a "distance ladder" and determine the distance from the Imaging Sciences building to downtown Rochester.
The methods you will use are
Each of these three steps introduces some uncertainty. You must estimate the uncertainty in each step, and the overall uncertainty in the distance to downtown Rochester.
You will need to go inside the Center for Imaging Sciences and up to its third floor to do part of this assignment. Make sure that you go there while the building is unlocked.
You must measure the distance from the front door of Building 76 to the seventh window of building 7B, the one with the bird feeder. Use your pace to measure the distance: figure out how far each of your paces is, then use your paces as you go from Building 76 to Building 7B. This might not be so easy. You can walk straight from Building 76 to the "tunnel", but you can't go straight through the shrubbery; you need to find some way to estimate the final segment of the distance, from the "tunnel" to the seventh window.
Write down the distance (in meters), and your estimate for the uncertainty in the distance, in terms of percent (that is, you might write 53 meters, plus or minus 5 percent).
The tallest dormitory on the RIT campus is Building 50, aka Ellingson Hall. You next job is to determine the distance from Building 76 to Building 50, without going there. Here's how:
angular size of seventh window in Building 7B R1 = ---------------------------------------------- angular size of windows in Building 50
dist to Bldg 50 = R1 * (distance to Building 7B)
Calculate the ratio R1, and also estimate an uncertainty in its value, in percent. Write down both the ratio and its uncertainty. Use your ratio to calculate the distance to Bldg 50, in meters.
In this step, you are using windows as standard yardsticks: objects which all have exactly the same size. They don't, in real life, so you calculation will be wrong; but at least it's a reasonable estimate.
In this step, you will assume that all big buildings are the same size, and use them as standard yardsticks. Again, it's not true, but it's better than nothing. Here's what to do:
apparent angular size of Building 50 R2 = -------------------------------------------- apparent angular size of downtown skyscraperand write it down
dist to downtown = R2 * (distance to Building 50)Calculate the distance to downtown Rochester, in meters.
Once again, you are making a somewhat dubious assumption: all big buildings are the same height. Once again, it's likely to be wrong --- but perhaps it's not wrong by too much.
So, what is your distance to downtown Rochester? Is it reasonable? Do you think it's correct?
In each step, there was some uncertainty. To figure out the overall uncertainty in the distance to Rochester, you need to add up the percentage uncertainty in each step:
total percent uncertainty = (percent uncertainty in step I) + (percent uncertainty in step II) + (percent uncertainty in step III)How large is your total uncertainty?
You can find the uncertainty in meters (instead of percent) by multiplying the percentage uncertainty by the distance to Rochester. So, for example, if you calculated
distance = 5000 meters total uncertainty = 25 percent uncertainty = (5000 meters) * (0.25) = 1250 meters ---> distance = 5000 +/- 1250 metersWrite down the uncertainty in your estimate, in meters.
Finally, use any device -- a map, a car, a GPS unit -- to find the REAL distance between the RIT campus and downtown Rochester. Compare that to your estimate. Was your value equal to the real distance, within your uncertainty?
Last modified by MWR, April 20, 2000
Copyright © Michael Richmond. This work is licensed under a Creative Commons License.