# The body, falling freely, reaches the ground in 5 seconds. How long would it take to reach the ground

**The body, falling freely, reaches the ground in 5 seconds. How long would it take to reach the ground if its initial speed was 5m / s?**

Task data: t1 (duration of the fall without initial velocity) = 5 s; Vн (initial speed) = 5 m / s.

Constants: g (acceleration due to gravity) ≈ 10 m / s2.

1) Fall height: h = g * t1 ^ 2/2 = 10 * 5 ^ 2/2 = 125 m.

2) The duration of the fall with an initial speed: h = Vn * t + g * t ^ 2/2.

g * t ^ 2/2 + Vn * t – h = 0.

10 * t ^ 2/2 + 5 * t – 125 = 0.

5t ^ 2 + 5 * t – 125 = 0 | : five.

t ^ 2 + t – 25 = 0 | : five.

D = 1 ^ 2 – 4 * 1 * (-25) = 101.

The roots of the equation (fall time): t2.1 = (-1 + √101) / (2 * 1) = 4.525 s (correct);

t2.2 = (-1 – √101) / (2 * 1) = -5.525 s (wrong).

Answer: With the initial speed, the body will fall in 4.525 s.