A certain freely falling object requires 1.25 s to travel the last 35.5 m before it hits the ground. From what height above the ground did it fall?

Answer 1

Let T be the time required to fall the entire height H. You will have to solve for both.

H = (g/2) T^2 = 4.9 T^2
H - 35.5 = (g/2)*(T-1.25)^2
= 4.9*(T-1.25)^2 = 4.9T^2 -12.25T + 7.656

Subtract the second equation from the first and solve for T. Then use that T to solve for H.

35.5 = 12.25T -7.7
T = 3.53 s

H = 60.9 m

Do it yourself and check my numbers; there could be a mistake.