We don't know anything about the amount of distance it travels, but that's okay. The only equation we need here is
velocity(final) = velocity(initial) + acceleration * time
vf = vi + (a * t)
The ball is dropped from rest, so vi = 0 m/s.
We want it so that the ball hits the ground with a final velocity of 60 m/s, so vf = 60 m/s.
We are given the acceleration due to gravity, a = 9.8 m/s^2.
We are solving for the time, t = ?.
Now we just plug in the values.
vf = vi + (a * t)
60 m/s = 0 m/s + (9.8 m/s^2)*(t)
60 = 9.8t
60 / 9.8 = t
t = 6.122 s
Hopefully this is the right answer.
