The “explosiveness” of a sprinter can not be trained in the weight room specifically. It must primarily be trained on the track. Explosive movements with weights help with strength, but not directly with sprinting power. It is a combination of strength and speed that gives the athlete power. Strenth and speed cannot be trained simultaneously as in “lifting weights fast” in order to gain sprinting speed, but must be trained in singularity. Train speed on the track and train strength in the weight room. For the sprinter, the track workout must come first. Whatever money is left in the energy wallet should be spent in the weight room.
Strength is simply the ability to generate maximal force.
Explosive strength is the ability to quickly achieve maximal force.
There’s an inverse relationship between force and velocity…in simple terms, strength-speed is explosiveness leaning towards maximal force, while speed-strength is explosivness leaning towards maximal velocity.
In both instances, you have starting-strength and acceleration-strength, which are, respectively, the ability to generate force (think of instantly “turning on” as many muscle fibers as possible) and the ability to maintain that force to peak levels.
The concept of power is the equilibrium between force and velocity, which is why it tends to fall in the 50-60% range of maximal force values.
Anyone needing to be “explosive” is advised to train all of these concepts in order to maximize potential, though the attention devoted to each will obviously vary according to the sport.
Additionally, reactive strength, which is the ability to absorb and reverse forces, should be trained as well. Although it is similar to the above qualities, it is defined as a discrete motor ability.
As far as transfer to sprinting, developing these qualities in the weight room will provide a base, but will do nothing for the skill itself. That has to be trained directly.
As far as methodology and sets/reps, that’s highly individual again, but the basic idea is going to be a lot of sets with low reps, performed with as much effort as can be used. The speed of the movement will vary according to the load used, but the idea is the same.
Concentric-only, static-dynamic, dynamic isometric, ballistics and throws, accomodating resistance (bands and chains), contrast training (think Poliquin’s 1-6 method), and just plain old CAT training are all ways to develop these characteristics.