Friday Puzzler -- Explorer on a walk

Re: Friday Puzzler -- Explorer on a walk

bill earl

At Bob's base camp

Maybe

Alex Y

but you are not told where that base camp is.

Re: Maybe

bill earl

But the question as stated is ambiguous.

Is he using a compass or a GPS to navigate?

Either way, the scenery is probably pretty much the same.

Re: Maybe

Alex Y

Is he using a compass or a GPS to navigate?

Either way, the scenery is probably pretty much the same.

But still, his base camp may not be the ideal location, even if you knew where that base camp was.

Re: Maybe

bill earl

Assuming that Bob's movements are restricted to the Earth's surface, the daily S-E-N expeditions of Bob are only possible in one coordinate system. And (without further clarification) the ideal radio location would be at the origin of that coordinate system. The question is, where is the origin of that coordinate system?

If he is using a GPS rather than a compass, that would imply the northernmost intersection of the lines of longitude.

Re: Maybe

Larry Barrett

If Bob's actual path was always the same, then a transmitter located at the center of the spherical triangle would require the least power. Of course, if his origin is as you point out, then Bob's route would not necessarily be the same each day.

Another possibility, albeit requiring a little navigational license, would be if Bob's base camp was 1 mile north of the southernmost intersection of the lines of longitude. He would then travel 1 mile south, march in place for the equivalent of a mile, turning to the east with each step, then return to his base camp. The transmitter would be located at the midpoint, 1/2 mile south of the base camp.

Re: Maybe

Alex Y

Assuming that Bob's movements are restricted to the Earth's surface

If he is using a GPS rather than a compass, that would imply the northernmost intersection of the lines of longitude.

Re: Maybe

Alex Y

Another possibility, albeit requiring a little navigational license, would be if Bob's base camp was 1 mile north of the southernmost intersection of the lines of longitude. He would then travel 1 mile south, march in place for the equivalent of a mile, turning to the east with each step, then return to his base camp.

At the north pole

charlie belden

which is where his base camp is

Re: Maybe

bill earl

If you knew which meridian upon which Bob set out upon each morning, you could refine the location. But without further clarification, you have to assume that he could choose any heading from 0-360 degrees. From the information provided so far, we know that the geographic north pole is the center of Bob's possible range.

Re: Maybe

Larry Barrett

If 'marching in place' is not allowed, there is another location, X, for Bob's base camp not far away that will work. Point X is located a little more than 1 mile north of the southernmost intersection of the lines of longitude (S pole) such that when Bob walks 1 mile south he reaches point Y. He then turns to the east and walks 1 mile, bringing him back to point Y (he circumnavigates the earth on this 1 mile walk), and he then turns north and walks 1 mile back to his base camp at point X. The distance from Y to the S pole will be approximately the radius of the 1 mile circumnavigation circle; so Y will be approximately 1/6 mile north of the pole, and X will thus be approximately 1 1/6 mile north of the pole.

Correct!

Alex Y

While there is one location in the northern hemisphere for Bob's base camp, there are infinitely many possibilities near the south pole. In fact, there are even infinitely many latitudes at which he could set up his base camp. It is at 1+1/(2*n*pi) miles from the south pole, where n is a positive integer, the number of circles he makes during his eastward trek.

So the answer to the original question is that you need to set up your communication station very close to the equator (either a few yards north or south of the equator, depending on whether you have to be able to reach him at base camp or only on his eastward treks.