This analysis is not perfect, since all of the splits required are not contained. I erred on Bolt's side in every bit I could where a discrepancy arose.
Usain Bolt - 6'5" elite sprinter, but poor outfielder instincts, takes a wrong step.
MikeT - 270 lb Defensive lineman prospect, who assumedly has good outfielder instincts.
Who gets to the ball first?
Considering you have 6'5" Bolt assumedly taking an entire wrong step before changing direction, we can compare the reaction time/change of direction speed between a 20 yard split (on a 40 yard dash) and a 20 yard shuttle, which features 2 changes of direction.
For the sake of easy conversion, I've decided they will be running 55 feet instead of 50 (as the original problem suggests).
MikeT - 55 foot sprint.
Bolt - 2.5 feet wrong direction, 180 degree turn, 57.5 feet sprint.
The best (20 yd or 5/10/5) shuttle took 4.00 at this season's combine (http://www.nfl.com/combine/top-performers#tp-tab-set-1:tp-grid-container-twenty-yard-shuttle). If you aren't familiar with the 20 yard shuffle, it takes place on grass. The player must sprint 5 yards, touch a line, turn 180 degrees, sprint 10 more yards, touch the other line, change direction again, and go back to their original position (5 more yards). It's called the 5/10/5 shuttle, and it's used to measure agility and change of direction/acceleration for NFL prospects.
Chris Johnson has the fastest 10 yard split in combine history at 1.4 (http://wiki.answers.com/Q/What_is_the_fastest_10_yard_split_in_the_40_yard_dash).
Assuming the best 10 yard split 4.0 total time - (1.4 (CJ 10 yd Dash) x 2 (20 yards not 10)) = 1.2. 1.2 / 2 change of directions = 0.6 to change direction comparing top athletes at the NFL combine with the best speed.
Bolt's 20 meter (21.87 yd) splits - 2.89. (http://1.bp.blogspot.com/_ua8ycqfc4ok/Sok0X9U62uI/AAAAAAAABq8/HJwymrWaDn4/s1600-h/Table.gif) Assuming he is not still accelerating, and taking his 20 meter time, adjusting it to 50 feet, is (which is in Bolt's favor), that he takes 2.64 seconds to run 60 feet. Add in an elite change of direction, estimated at (0.6), and neglecting both the acceleration for those 5 feet twice, and basing his total time on a higher average speed than attainable (at 55 ft), we've got a 3.24 second extremely optimistic estimate to complete the above for Bolt.
The combine is hand-timed, while Olympic sprints are timed from the gun electronically. Since the athlete determines when to start (the 40) in the combine, an average error of a human is 0.25 seconds, so I'll be adding that into MikeT's combine times.
MikeT will be 274 lb unsigned DT prospect (MIKE bennetT) (http://en.wikipedia.org/wiki/Michael_Bennett_(defensive_tackle) ) running a 5.00 40 yard sprint, with a 2.84 20 yard sprint. (Adjusting for combine hand timing, average error of 0.25) = 3.09 20 yard sprint. Adjusting this to 55 feet (similar conversion as Bolt's) would be 2.83.
Assuming Bolt is the "best" at these other drills (which is a stretch considering Bolt doesn't even reach his top speed during his first 40 meters, much less his first 20). Also, we are assuming that Bolt is elite in agility, which probably isn't the case, since reaction time/change of direction have nothing to do with sprinting, it's just acceleration/top speed... and taking every liberty in Bolt's favor.
Usain Bolt - 3.24
MikeT - 2.83
MikeT wins by a couple of steps. Even if Usain had "best ever" reaction times to the ball being hit, this doesn't make up for the bad step or the 0.41 second that the huge/slow player takes to get there. (average reaction time somewhere around a quarter of a second).