Two diamonds begin a free fall from rest from the same height 0.9 s apart. How long after the first object begins to fall will the two objects be 11 m apart?

Answer 1

Let t=0 be the time the first one is dropped. The distance that it falls after that is
y1 = (g/2)t^2 = 4.9 t^2
The distance that the second one has fallen at time t(>0.9s) is
y2 = (g/2)(t-0.9)^2 = 4.9(t-0.9)^2

You want to solve for the time t when
y1 - y2 = 4.9 [t^2 - (t-1)^2] = 11 m

2t - 1 = 11/4.9 = 2.24 s
t = 1.62 s

Answer 2

Two diamonds begin a free fall from rest from the same height 1.2 s apart. How long after the first object begins to fall will the two objects be 20 m apart?