Assignment 5: Measure a distance with parallax

Due Monday, Apr 17, 2000, at the beginning of class

Your job this week is to use parallax to measure the distance from a bench outside Building 76 to the official RIT flagpole.

Go to the main entrance of Building 76. You will find a bicycle rack to the left of the main doors, and a bench a bit further to the left. Your job is to measure the distance from this bench to the official RIT flagpole, which is visible beyond the parking lots to the North-East.

If you stand under the lamp next to the walkway to Building 7, and look towards the flagpole, you will see in the distance three skyscrapers in downtown Rochester. The tallest of the three is a dark building which appears furthest to the right (the others are a shorter building in the middle, and a tall, light-colored building on the left). Use this tall, dark building as a reference.

You will need to devise some method of measuring angles between two distant objects, in units of degrees. If you can't think of a way to measure angular distances, visit me during my office hours and ask.

Explain, in detail, step-by-step, exactly how you are making these angular measurements. Draw pictures, if it will help.

Now, calculate the distance to the flagpole by following these steps.

Measure the distance along a line joining the bicycle rack and the walkway lamp, in meters. This will be your baseline distance.
Stand under the walkway lamp. Look at the flagpole, and look past it at the tall, dark skyscraper. Measure the angle between the flagpole and the dark skyscraper, in degrees. This should be a small angle -- the flagpole and the skyscraper should be close together.
Stand next to the bicycle rack. Again look at the flagpole. Measure the angle between the flagpole and the dark skyscraper, in degrees. It should be a much larger angle than before.
Calculate the total angle by which the flagpole appears to have moved, as seen from the two ends of the baseline. Express this angle in degrees. This total angle is indicated in the diagram above, with the Greek letter theta.
Draw a diagram of the situation. Label the baseline distance, the angles you measured, and theta.
Use the length of the baseline in meters, and the angle theta, to calculate the distance to the flagpole in meters.

Look at your result -- does it make sense? Can you think of some way to check the estimated distance? If so, go ahead and check it. How accurate was your calculation?

What is the uncertainty in your measurement of the baseline distance? What is your uncertainty in the measurement of angles? Which type of measurement leads to a greater uncertainty in the final result? How could you improve the measurement?

Last modified by MWR, April 12, 2000