The A Train makes the longest run of any subway in the New York City Transit system. The stretch from 207 Street to Broadway-Nassau is just about as long as the entire island of Manhattan. The data in the accompanying text file were taken from the 2008 weekday schedule for the A Express Train.
- Add two new columns to the data table.
- Use the time of day given in the timetable to determine the time elapsed in hours.
- Use the fact that the numbered streets in Manhattan are spaced 20 per mile and determine the distance traveled in miles.
- Construct a distance-time graph with a line of best fit and use it to determine the following quantities in Anglo-American units …
- the average speed of the A Train.
- the length of Manhattan.
- the length of the A line.
- jet-takeoff.txt, jet-landing.txt
One fine day, a Boeing 717 departed from Mitchell International Airport (MKE) in Milwaukee. Approximately two hours later, it arrived at LaGuardia Airport (LGA) in New York. During takeoff and landing, runway positions (in meters) were recorded as a function of time (in seconds) and the data were saved as tab-delimited text files. Using the data in these files and your favorite graphing software …
- construct a graph of distance vs. time for…
- takeoff and
- then fit a quadratic curve to the data so that you can determine …
- the acceleration at takeoff and
- the deceleration on landing
- and also determine …
- the final speed when the airplane left the runway in Milwaukee and
- the initial speed when the airplane hit the runway in New York
- A picket fence is a type of fence (obviously). This kind of fence is made out of evenly spaced, vertically aligned, pointed slabs of wood tied together near the top and bottom by cross members. A picket fence is also the name of a piece of laboratory equipment used by introductory physics students. This kind of "fence" is a transparent piece of plastic with opaque bands spaced evenly across it. When this kind of picket fence passes through a photogate, the opaque and transparent bands can be used to determine position as a function of time.
The second kind of picket fence was used for two experiments. In the first experiment, the picket fence was allowed to fall freely through a photogate. In the second experiment, the picket fence was given a push upward and then allowed to pass freely through a photogate. Use the position–time data from each experiment to determine the acceleration due to gravity on the surface of the earth.
The Hawaiian Island chain is more than just the visible islands. It also includes the Emperor Seamounts. (Seamounts are islands that have eroded down below sea level.) The combined Hawaii–Emperor chain is a series of volcanic structures formed by a single, long-lived plume of magma referred to as a "hotspot". The hotspot stayed fixed as the pacific plate slowly moved over it, resulting in a chain of volcanoes stretching from the Aleutian Islands off the coast of Alaska to Mount Kilauea on the Big Island of Hawaii. Use this data to determine the speed of the Pacific plate. The columns in this data set are as follows:
- volcano number
- volcano name
- volcano age (millions of years)
- distance from Kilauea (km)
- uncertainty in age (millions of years)
- uncertainty in distance (km)
Source: D.A. Clague & B.G. Dalrymple. "Tectonics, geomorphology and origin of the Hawaiian-Emperor volcanic chain." The Eastern Pacific Ocean and Hawaii. Eds., E.L. Winterer, D.M. Hussong, R.W. Decker. Boulder, CO: Geological Society of America (1989): 188-217.
The Indian Space Research Organisation (ISRO) launched the Mars Orbiter Mission from the Satish Dhawan Space Centre in Andhra Pradesh on 5 November 2013. The Mars Orbiter Spacecraft has been given the nickname मंगलयान (transliterated to Maṅgalayāna or Mnglyan), which is Sanskrit for "Mars craft". English speaking news agencies have been writing this as "Mangalyaan".
The launch system used was an "extended" version of the four-stage Polar Satellite Launch Vehicle (PSLV-XL) built by ISRO. The launch number for the Mars Orbiter Mission was C25. The accompanying text file gives velocity-time data at significant moments of the PSLV–C25 launch taken from a page on the ISRO website. Use this data to solve the following problems.
- Contruct a velocity-time graph of the launch.
- Using a line of best fit, determine the average acceleration from first stage ignition to third stage separation (i.e., the portion of the data set where the acceleration is most nearly uniform).
- Using numerical integration, create a distance-time graph from first stage ignition to spacecraft separation (i.e., the whole data set).
For the more advanced student.
- Fit an exponential approach curve to the data from first stage ignition to third stage separation (the same range of values used for part b of this problem).
- Using the results of your curve fit, derive an expression for acceleration as a function of time.