Actually I just worked a problem using Nick Newman’s numbers and it seems very accurate. You have to take into consideration that the optimal take-off angle for a long jumper is ~21 degrees.
I looked at Nick’s log and his best long jump is 7.54m and I believe he said somewhere he runs a 10m fly in ~.95 seconds. I’m going to use Nick’s 10m fly velocity as his take off velocity, or Vo.
First solve for time in the air: (I’m using upper case for variables and lower case as subscript)
Vy = Voy*sin() + Ay*Tup
0 = 10.526*sin(21°) + (-9.8)*Tup
Tup = ~.385 seconds
Ttot = ~.770 seconds
Now solve for distance / range:
X = Vx*cos()*Ttot
X = 10.526*cos(21°)*.770
X = 7.565m
7.565m is pretty close to 7.54m, and if you were to take air resistance into account it would probably be even more accurate.