Stevarino: "But will our initial velocities be equal?"

Good point. Part of the force made by our muscles while jumping is to overcome our weight. Most of the force, however, is to overcome our inertia (since we accelerate up at more than 1G while jumping). Remember that, on the moon, you might have less gravity to overcome, but you have just as much inertia.

If, while jumping up, your body accelerates up at 3g, then on the moon it would be about 3 5/6 g, but over a shorter period of time (same distance, if you jump the same way). So yeah, you should leave the ground a little faster, but not much. One way to find out would be for someone to wear a harness that allows them to hang from a giant pendulum while lying down horizontally, and then have them push off from a wall as hard as they can. Their speed would be closer to moon jumping speed than vertical earth jumping speed.

"If you jump in orbit, you'll just end up in a more elliptical orbit"

Not necessarily. If you jump in orbit in the upwards/downwards direction, or along the direction of the orbit, you'll end up in a more elliptical orbit (or in a LESS elliptical orbit, if you time it right). But if you jump in the sideways direction with some component along the direction of the orbit, you might just change your inclination (i.e. you might just change your orbital axis, but keep the same orbit shape, just tilted differently).

"Does the word "Jump" also incorporate the word "Land"?"

Neglecting air resistance, you always land at the same speed you left the ground, but going in the opposite direction.

"Again, all of you people saying that you can jump six times higher on the moon are WRONG... you WOULDN'T be wearing heavy boots, a space helmet, padded jumpsuit, and oxygen tanks."

All right. Then, on the moon while wearing a spacesuit, you can jump six times higher than you can jump on earth while wearing a spacesuit. Well, a little more than 6 times since your jumping speed will be a little higher (less weight, same inertia) and you'd have no air resistance.

"You can't actually jump six times as high as on earth, you can only raise your center of gravity by six times as much as on earth"

Hopefully, when my center of gravity moves by some distance, the rest of my body follows! If my center of gravity goes up by a foot, my feet also go up by a foot, and so does my head. If my center of gravity goes up six feet, so do my feet, and so does my head. Unless I try to perform a flip or something. And yes, I know that the athletes who do high-jumps arc their bodies so that their bodies go over the bar even though their CG might not. But still, it would all be 6x as high (or a little more) on the moon as on the earth.

"The bag doesn't say anything about what happens after time t6."

Good point... The bag is right after all... ;)