Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - Guided Practice for Examples 6 and 7 - Page 287: 16

$102$ feet.

Similarly as in the example: $y=-16t^2+80t+2\\y=-16(t^2-5t)+2\\y+(-16)(2.5)^2=-16((t-2.5)^2)+2\\y-100=-16(t-2.5)^2+2\\y=-16(t-2.5)^2+102$ So the vertex is at $(2.5,102)$; thus the maximum height is $102$ feet.