A free-falling body has passed 196 m in the last 4 from the fall. How long did the body fall?

t4 = 4 s.

S4 = 196 m.

g = 9.8 m / s2.

t -?

Since the body falls freely, its initial velocity is V0 = 0 m / s. The body moves uniformly accelerated with gravitational acceleration g.

Let us assume that the entire time of the fall of t is = x s.

S = g * t2 / 2.

t = √ (2 * S / g).

S1 = g * t1 ^ 2/2 = g * (t – t4) ^ 2/2 = g * (t – 4) ^ 2/2.

S4 = S – S1 = g * t ^ 2/2 – g * (t – 4) ^ 2/2.

2 * S4 / g = t ^ 2 – (t – 4) 2 = t ^ 2 – (t ^ 2 – 8 * t + 16) = t ^ 2 – t ^ 2 + 8 * t – 16 = 8 * ( t – 2).

t – 2 = S4 / 4 * g.

t = 2 + S4 / 4 * g.

t = 2 + 196 m / 4 * 9.8 m / s2 = 7 s.

Answer: the fall of the body lasted t = 7 s.