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Mon 21 Nov, 2005 09:13 pm
Hi all! I don't know how to do this problem:
The designer of a 30 ft diameter spherical hot air balloon wants to suspend the gondola 8 feet below the bottom with cables tangent to the surface to the balloon. Two of the cables run from the top edges of the gondola to their points of tangency (-12,-9) and (-12,9)
x^2+y^2=225
How wide should the gondola be?
If he has a 4 ft gondola and attached the wires, where should the cables be attached to the balloon so that the cables are still tangent to the surface of the balloon?
Please help! Thanks!
There's only one line tangent to a circle at a given point. It is perpendicular to the radius at that point.
Where does that line intersect a horizontal line 8 feet below the bottom of the circle.
For part 2, I see a right triangle with legs 23 and 2 (half the width of the gondola). The hypotenuse is also the hypotenuse of a right triangle with legs 15 (radius at tangent) and the length of the wire.
Draw a picture and label all of the lengths and angles (from similar triangles) you know, then solve for the unknowns.
Obviously this is a mathematical problem and not an engineering one. Anyone who doesn't know that hot air balloons are usually tear-drop shaped while gas balloons are spherical, all the cables run from the top of the balloon down to the gondola, and that you must take the compressibility of the balloon envelope and the forces of gravity into consideration (so cables are never mathematically tangent) should not be designing balloons.
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