NAME_________________________________ CLASS____________________ DATE____________

- What is the length of a Boeing 747-400 domestic airplane?
Length = __________

- Let us suppose that the approximate weight distribution
(function) on a loaded 747-400 domestic airplane is given by the
equation,
w(x) = 700 sin(2px / L) + 42,850,

where x is the distance measured from the nose of the airplane. Graph the weight distribution.

- What is the total weight W of the airplane?
- Use the equation,
to calculate the center of gravity of the airplane. The integration is calculated for x = 0 (nose) to Length (tail).

[

**Hint**: Use integration by parts.]cg = __________________

- Let us suppose that the approximate weight distribution
(function) on a loaded 747-400 domestic airplane is given by the
equation,
w(x) = 777 ( cos(2px / L) + sin(2px / L) ) + 42,850, where x is the distance measured from the nose of the airplane. Graph the weight distribution.

- What is the total weight W of the airplane?
- How does the weight calculated in Problem 3 compare with the
weight in Problem 6?
__Explain why this is so__.Use the equation,

to calculate the center of gravity of the airplane with the new weight distribution. The integration is calculated for x = 0 (nose) to Length (tail). [

**Hint**: Use integration by parts.]cg = _____________

- Did the center of gravity move?
- If so, did it move toward the airplane's nose or
tail?
- If not, why did it stay in the same position?

- If so, did it move toward the airplane's nose or
tail?
- If the airplane's center of gravity moved significantly during
flight, do you think the pilot would notice it?
__Why or why not?__