With what time interval did two drops detach from the roof, if, after 4 s from the beginning

With what time interval did two drops detach from the roof, if, after 4 s from the beginning of the fall of the second drop, the distance between the drops is S = 20 m.

Initial data: t2 (elapsed time after the fall of the second drop) = 4 s; ΔS (distance between drops after 4 s) = 20 m.

Constants: g = 10 m / s ^ 2 = a.

1) Distance covered by the second drop (drop free fall):

S2 = g * t2 ^ 2/2 = 10 * 4 ^ 2/2 = 80 m.

2) Distance covered by the first drop:

S1 = S2 + ΔS = 80 + 20 = 100 m.

3) Falling time of the first drop:

S1 = g * t1 ^ 2/2; t1 = √ (2S / g) = √ (2 * 100/10) = 4.47 s.

4) Time Lapse:

Δt = t1 – t2 = 4.47 – 4 = 0.47 s.