what about for sprinting>
Depends on whether you mean speed or actual sprinting. In general increasing your squat will help you more in two-footed standing jumping than it will in running. Squatting will usually have some carryover to the acceleration phase of sprinting. For speed relevant to sport (soccer, football, etc) this is about all that matters. However, for actual sprinting the acceleration phase is a minor part of the race. Most high level sprint races separate when athletes get the chance to display max velocity. The problem with this is that if your increases in the squat are combined with increases in bodyweight your maximum velocity may suffer EVEN if your relative strength (as measured by squat to bw) increases. If you plan on competing as a sprinter... watch out for this.
For a track sprinter, what would you prescribe to improve maximum velocity and how do you explain lower speed despite improved relative strength?
Maximum velocity is by far the hardest quality to train. It's equal part tendon stiffness and leg strength. For well trained athletes max V can be improved with overspeed work (pulling, slight downhill runs, etc), lot's of max V work (flying 20s, etc), single leg bounding work, or changes to mechanics.
It's lower speed despite improved relative strength as measured by the squat. You see this because the squat becomes a poor measure of strength at maximum velocity. Even high school sprinters have their fastest 10-meter splits well under a second. At this speed an athlete must exhibit extremely brief powerful single leg ground contact and the squat does not accurately predict their ability to produce power in this movement. So basically, if you weigh 150 pounds and squat 300 pounds and run an 11 flat 100m (assume fastest 10m split of 0.9) and you increase your back squat to 400 pounds and your bodyweight to 200 pounds it's very likely that your 10m split will now be slower.
Note that this is less true for poorly trained athletes. If an athlete is running 13.0 seconds in the 100m then their max V may likely simply because they fatigue before they can accelerate to max V. If this is the case then overdistance work for endurance and increase in relative strength as measured by squat will increase their acceleration, maximum velocity and speed endurance.
Notice that this is less true for an untrained athlete.