If the first ball survives the 14 floor drop then drop it again from the 27th (14+13) floor. If it breaks you can determine the exact breaking point with at most 12 more droppings.

If the first ball survives the 27 floor drop then drop it again from the 39th (14+13+12) floor. If it breaks you can determine the exact breaking point with at most 11 more droppings.

Keep repeating this process always going up one less floor than the
last dropping until the first ball breaks. If it breaks on the x^{th} dropping you will only need at most 14-x more droppings
with the second ball to find the breaking point. By the 11th dropping
of the first ball, if you get that far, you will have reached the
99th floor.

Thanks to Alon Amit for this problem.

Michael Shackleford, A.S.A., 10/31/1998