13 replies to this topic

[3ala2]

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.

[Tonybz]

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.

[mojail]

Spoiler for Answer

X = 45

[3ala2]

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.

[3ala2]

well.. i didn't think it would be that hard...

[ljb]

Clarification? The problem states the plane starts at 0 and goes straight for X meters. However, the provided picture shows 12X. Which is correct?

[plainglazed]

It does seem that there are some inconsistencies here

Spoiler for but

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=75.805^o? 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 .

[3ala2]

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

Spoiler for Hint

The diagram can be very helpful (top view)

[3ala2]

It does seem that there are some inconsistencies here

Spoiler for but

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=75.805^o? 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.

[ljb]

Spoiler for going off the diagram I got

x = arccos(11/12) = 23.55646430917

Any chance we can see your solution + work?