Is about a 45 degree angle of elevation for the cue correct? For most practical shots, it will be less than 45 degrees. It depends on how much of the ball you need to clear and how soon. Should I hit the cue ball right in the center or a little above center? Below center is better, but not so low you miscue, which is a foul on jump shots, at least at nine ball. If you hit above center, the cue stick tends to trap the cue ball on the cloth. Rule 3.24 says it is illegal to "dig under" the ball to get it to jump. Hitting the cue ball below center is not "digging under". By "digging under" I assume they mean a miscue. Miscues are illegal by rule 3.25. Should I stroke through the cue ball, or does that interfere with the cue ball jumping? You need to use a somewhat shorter stroke to avoid hitting the cloth. If you are already slowing the cue down at the instant of contact, it will act as if it were lighter, which is better. Does it have to be hit extremely hard? It depends on the distance from the cue ball to the obstruction, the weight of the cue stick, and how much of the obstruction you need to clear. The cue ball's path while in the air is a parabola, and you can calculate how fast the ball must be going to just clear the obstruction at the peak of the trajectory. The most important factor is the kind of cloth on the table. If it is very high quality, thin cloth, jumping will be very difficult. If it is thicker or maybe rubber-backed, jumping will be easy. Start with an easy drill: Freeze three balls together in a line parallel to and about a foot from a rail. Remove the middle one. Place the cue ball an inch from the rail, and shoot it through the hole. Twenty degrees elevation should be plenty for this shot. Do the same, but place an object ball to be pocketed after the jump. Move the two obstructing balls closer to each other and/or farther from the cue ball. Can I make an object ball jump over an obstruction? Yes, this is the "double jump." If the cue ball is in the air when it hits the object ball, the object ball will jump some. Details are left as an exercise for the reader. At snooker, it is a foul for the cue ball to jump over a ball, whether intended or not (unless the cue ball has already struck an object ball)

The origanal answer is close but, you must hit the top half of the ball for a jump shot to be legal (center line or above). If you hit below center line to make the jump it is a foul and you just handed your opponent the ball and more than likely the game.

get a jump cue and go to http://www.engr.colostate.edu/~dga/pool/normal_videos/index.html

Actually, both previous answers are correct to a degree. When shooting with a nearly level cue it is illegal to make the cueball jump another ball by hitting it at the lowest point, essentially scooping it up. I tis also impossible to make the cueball jump over another object ball when shooting with a level cue. Jump shots can be made without a special jump cue. The jump cue just makes the shot easier as it is engineered for that specific task and a jump cue gives the player a wider range of jump shots. Essentially to jump a ball you need to be approaching the cueball at about a 45 degree angle or more with a full cue. You want to hit the cueball crisply and follow through. As said previously, when you approach the cueball at any angle your will have a centerline where you can hit above or below center. With a full cue jump you generally want to hit below center one to two tip's worth. With a jump cue you can hit above center and still jump the cueball.