What direction would?

Great Circle route: 41.45°, 6729.6 mi

Latitude and longitude of Fayetteville = 36.1 N, 94.2 W.

Lat & long of Jerusalem = 31.8 N, 35.2 E.

Because Jerusalem is slightly closer to the equator than Fayetteville is, you might THINK that the right way to face J from F would be slightly south of east.  You'd be wrong.

The latitude circles, if you are traveling eastward, curve continuously to the left, whereas we are looking for a direct route that goes straight over the horizon without turning left or right.

Consider a triangle whose vertices are F, J, and N (the N being 90.0 north, the pole).  Angle FNV is 94.2 + 35.2 = 129.4 degrees.  Side j (opposite vertex J) is 90 - 36.1 = 53.9 degrees.  Side f (opposite vertex F) is 90 - 31.8 = 58.2 degrees.  Side n (the shortest air route) is found from the spherical law of cosines:

cos(n) = cos(f)cos(j) + sin(f)sin(j)cos(N)

= cos(58.2)cos(53.9) + sin(58.2)sin(53.9)cos(129.4)

= -0.125392 => n = 97.2 degrees.

Then, to find the heading from F to J, we use the spherical law of sines:

sin(F)/sin(f) = sin(N)/sin(n) =>

sin(F) = sin(58.2)*sin(129.4) / sin(97.2) = 0.661960 =>

angle F (at Fayetteville) = 41.4 degrees.

This provides the rather startling result that if you want to face Jerusalem along the shortest route over the horizon, you should face 41 degrees NORTH of east.  Weird, huh ?