To find the time it takes for an object to fall a height of 78m, we can use the kinematic equation:

Vf^2 = Vo^2 + 2gh

Since the final velocity $Vf$ of the object when it hits the ground is 0 m/s, we can rearrange the equation to solve for time $t$:

2gh = Vf^2 - Vo^2
2gh = 0^2 - 0^2
2gh = 0

Now we can solve for time:

2gh = 0
2 9.8 78 = 0
1562.4 = 0
time $t$ = √$2h/g$

Plugging in the values:
t = √$2\ast 78/9.8$ t = √$156/9.8$ t = √15.918367346938775
t ≈ 3.9937285905787475

Therefore, it will take approximately 3.99 seconds for the object to fall a height of 78m.