Determine the time of the body falling to the ground if in the last 2 seconds it has passed 60 m.

Determine the time of the body falling to the ground if in the last 2 seconds it has passed 60 m. With what speed the body fell.

V0 = 0 m / s.

g = 10 m / s2.

t2 “= 2 s.

S2 “= 60 m

V -?

t -?

The body fell under the action of gravity, so it moved with the acceleration of gravity g and the initial speed of movement was V0 = 0 m / s.

The path covered by the body in the last 2 seconds S2 “is expressed by the difference: S2” = S2 – S1, where S2 is the path of the body for the entire time of movement, S1 is the path of the body for the entire time of movement without two seconds.

S2 = V0 * t + g * t ^ 2/2 = g * t ^ 2/2.

S1 = V0 * (t – 2) + g * (t – 2) ^ 2/2 = g * (t – 2) ^ 2/2 = g * (t2 – 4 * t + 4) ^ 2/2 = g * t ^ 2/2 – 2 * t * g + 2 * g.

S2 “= g * t ^ 2/2 – g * t ^ 2/2 + 2 * t * g – 2 * g = 2 * t * g – 2 * g.

2 * t * g = S2 “+ 2 * g.

t = S2 “/ 2 * g + 1.

t = 60 m / 2 * 10 m / s2 + 1 = 4 s.

V = V0 + g * t = g * t.

V = 10 m / s2 * 4 s = 40 m / s.

Answer: the fall of the body lasted for a time t = 4 s and at the moment of impact had a velocity of V = 40 m / s.