s = 96t−16t^2
For the first part... let s = 128 ......so we have.....
128 = 96t - 16t^2 divide through by 16
8 = 6t - t^2 rearrange as
t^2 - 6t + 8 = 0 factor
(t - 4) )( t - 2) = 0
So
t - 4 = 0 or t - 2 = 0
add 4 to both sides add 2 to both sides
t = 4 t = 2
So.....it will be 128 ft above the ground after 2 seconds and after 4 seconds ...it is falling at the 4 second mark
For part (b), when it hits the ground, s = 0
So....see if you can solve this
0 = 96t - 16t^2
Let me give you a hint......if it takes 2 seconds to reach a height of 128 ft....it will also take 2 more seconds to reach the ground after reaching the 128 ft mark for the second time