Guest Posted November 4, 2009 Report Share Posted November 4, 2009 A plane moves from point 0 and travels in a straight horizontal line a distance of X meters before it flies a distance of 17X in the same direction making with the earth line an angle X degrees. Then in the moment the pilot decides to maintain a constant latitude he turns anticlockwise with a certain angle and radius, and flies horizontally in the new direction for a distance of 18X before he lands to the starting point 0 by an angle of 3X/2. I think that's all the info needed. Find X. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 4, 2009 Report Share Posted November 4, 2009 The description of events is a bit unclear, especially the last part "flies horizontally in the new direction for a distance of 18X before he lands to the starting point 0 by an angle of 3X/2." A diagram might help. Thanks. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 4, 2009 Report Share Posted November 4, 2009 X = 45 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 4, 2009 Report Share Posted November 4, 2009 The description of events is a bit unclear, especially the last part "flies horizontally in the new direction for a distance of 18X before he lands to the starting point 0 by an angle of 3X/2." A diagram might help. Thanks. this is a top view diagram.. hope it makes it easier to understand. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 6, 2009 Report Share Posted November 6, 2009 well.. i didn't think it would be that hard... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 6, 2009 Report Share Posted November 6, 2009 Clarification? The problem states the plane starts at 0 and goes straight for X meters. However, the provided picture shows 12X. Which is correct? Quote Link to comment Share on other sites More sharing options...
0 plainglazed Posted November 6, 2009 Report Share Posted November 6, 2009 It does seem that there are some inconsistencies here as I read the problem, I'm not sure that they are material. Maybe there are just two triangles to compare and the rest is red herring. Both triangles start at ground level and reach the same height. One triangle with an angle(X) and hypotenuse 17X and the other with an angle(3X/2) and hypotenuse 18X. Then 17sin(X)=18sin(3X/2) and I get X=75.805o? Kind of hard to visualize a plane climbing at an angle for a prescribed distance, circling at a constant elevation, and then descending at a steeper angle over a greater distance than the initial climb and the result not be affected by the distance between the point of initial climb and the endpoint though so I suspect I'm way off . Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 6, 2009 Report Share Posted November 6, 2009 Clarification? The problem states the plane starts at 0 and goes straight for X meters. However, the provided picture shows 12X. Which is correct? Sorry for this mismatch.. 12X is the correct distance The diagram can be very helpful (top view) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 6, 2009 Report Share Posted November 6, 2009 It does seem that there are some inconsistencies here as I read the problem, I'm not sure that they are material. Maybe there are just two triangles to compare and the rest is red herring. Both triangles start at ground level and reach the same height. One triangle with an angle(X) and hypotenuse 17X and the other with an angle(3X/2) and hypotenuse 18X. Then 17sin(X)=18sin(3X/2) and I get X=75.805o? Kind of hard to visualize a plane climbing at an angle for a prescribed distance, circling at a constant elevation, and then descending at a steeper angle over a greater distance than the initial climb and the result not be affected by the distance between the point of initial climb and the endpoint though so I suspect I'm way off . well maybe this is something to start with. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 13, 2009 Report Share Posted November 13, 2009 x = arccos(11/12) = 23.55646430917 Any chance we can see your solution + work? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 14, 2009 Report Share Posted November 14, 2009 this is a top view diagram.. hope it makes it easier to understand. working in 2D will make it much easier reference to the sketch, and knowing that two tangents fom one point to the same circle have the same length, then, regardless to the radius of the circle, the two horizontal projections (which are the two tangents) are of the same length which means 12x + 17x(COSx) = 18x + N COS(3x/2) [eq.1] N is the length of the last portion (landing back to 0) having the angle withn the ground 3x/2 to find N, we consider the plane reaches to a constant height, and keeps horizontal till landing, which means 17x SINx = N SIN(3x/2) => N = 17x SINx / SIN(3x/2) in [eq.1], 6x + 17x (SINx COT(3x/2) - COSx) = 0 this has certailnly a solution x=0, but as we need a different solution, we consider x > 0 and 17(SINx COT(3x/2) - COSx) + 6 = 0 to find x we... or maybe i'll stop here to see wat u have to say abt this. FIND X. 17(SINx COT(3x/2) - COSx) + 6 = 0 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 16, 2009 Report Share Posted November 16, 2009 3ala2 - I agree with your work... arccos(11/12) is a solution to your halfway equation Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 16, 2009 Report Share Posted November 16, 2009 3ala2 - I agree with your work... arccos(11/12) is a solution to your halfway equation Good job ljb, this is the correct answer. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 16, 2009 Report Share Posted November 16, 2009 (edited) you already gave the correct answer in post #10.. hmm Edited November 16, 2009 by 3ala2 Quote Link to comment Share on other sites More sharing options...
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A plane moves from point 0 and travels in a straight horizontal line a distance of X meters
before it flies a distance of 17X in the same direction making with the earth line an angle X degrees.
Then in the moment the pilot decides to maintain a constant latitude he turns anticlockwise with a certain angle and radius,
and flies horizontally in the new direction for a distance of 18X before he lands to the starting point 0 by an angle of 3X/2.
I think that's all the info needed. Find X.
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