This project is adapted from the article \How Not to Land at Lake Tahoe!" by Richard Barshinger (The AMS
Monthly, 1992 ).
3. To avoid a sense of weightlessness or feeling of being crushed during landing, the magnitude
of the acceleration of the plane should always be (much) smaller than the acceleration due
to gravity. More precisely, with 0 < M < g, we require abs(a(x)) is less than or equal to M for each x in the interval
[a1; b1]. Provide a condition on H, L and S that ensures this requirement is satisfied.
so far our equation is 0< S[((12H/L^4)x^3) + ((24H/L^3)x^2) + ((12H/L^2)x)] < M
but we're not sure if this is correct. There is also this problem that deals with it:
4. On a flight from Omaha to New York, the plane has a cruising altitude of 37,000 feet with a
speed of 600 miles per hour. The flight begins its descent near Scranton, Pennsylvania, which
is about 130 miles from New York. Is the condition you found in problem 3. satisfi ed? What
is the plane's maximum (magnitude of) acceleration during the approach to the airport?
What is the maximum magnitude of the plane's rate of descent? At what point (near what
town or city) would the descent need to begin if the magnitude of acceleration should be
kept below 0.1 feet/sec2?
Monthly, 1992 ).
3. To avoid a sense of weightlessness or feeling of being crushed during landing, the magnitude
of the acceleration of the plane should always be (much) smaller than the acceleration due
to gravity. More precisely, with 0 < M < g, we require abs(a(x)) is less than or equal to M for each x in the interval
[a1; b1]. Provide a condition on H, L and S that ensures this requirement is satisfied.
so far our equation is 0< S[((12H/L^4)x^3) + ((24H/L^3)x^2) + ((12H/L^2)x)] < M
but we're not sure if this is correct. There is also this problem that deals with it:
4. On a flight from Omaha to New York, the plane has a cruising altitude of 37,000 feet with a
speed of 600 miles per hour. The flight begins its descent near Scranton, Pennsylvania, which
is about 130 miles from New York. Is the condition you found in problem 3. satisfi ed? What
is the plane's maximum (magnitude of) acceleration during the approach to the airport?
What is the maximum magnitude of the plane's rate of descent? At what point (near what
town or city) would the descent need to begin if the magnitude of acceleration should be
kept below 0.1 feet/sec2?