# In the first second of its fall without initial velocity, the body covered 1/36 of the entire path. How many seconds did the body fall?

1) Let us calculate the height from which this body fell (we assume that the fall of this body was free):

S1 = h = a * t1 ^ 2/2, where S1 is the distance that the body will cover in the first second of the fall (S1 = 1/36 S), and is the Acceleration with which the body fell (a = g = 10 m / s ^ 2), t1 is the fall time (t1 = 1 s).

1/36 S = g * t ^ 2/2.

S = 18g * t ^ 2 = 180 * 10 * 1 ^ 2 = 180 m.

2) Let’s calculate the fall time:

S = g * t ^ 2/2; t ^ 2 = 2S / g; t = √ (2S / g).

t = √ (2 * 180/10) = √36 = 6 s.

Answer: This body fell for 6 seconds.

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