The body was thrown down from the 6th floor with an initial speed of 18 km / h, find the time for

The body was thrown down from the 6th floor with an initial speed of 18 km / h, find the time for which the body flew to the ground. Take the height of the floor equal to 5m.

n = 6.

V0 = 18 km / h = 5 m / s.

h1 = 5 m.

g = 10 m / s2.

t -?

The body is acted upon only by the force of gravity m * g, so it will move with the acceleration of gravity g,

The time of the body’s fall is expressed from the formula for the body’s acceleration g: g = (V – V0) / t, where V is the body’s velocity at the moment of impact on the ground.

t = (V – V0) / g.

The velocity of the body at the moment of impact V is expressed from the formula: h = (V2 – V02) / 2 * g, where h is the height of the body’s fall.

h = n * h1.

V ^ 2 – V0 ^ 2 = 2 * g * n * h1.

V = √ (V0 ^ 2 + 2 * g * n * h1).

V = √ ((5 m / s) ^ 2 + 2 * 10 m / s2 * 6 * 5 m) = 18 m / s.

t = (18 m / s – 5 m / s) / 10 m / s2 = 1.3 s.

Answer: the body will reach the ground in time t = 1.3 s.