The crane lowers the load vertically down at a speed of 4 meters per second

The crane lowers the load vertically down at a speed of 4 meters per second when the load is at a height of 28 meters it breaks off and the load falls to the ground.

Data: V0 (speed of movement of the load until the cable breaks) = 4 m / s; H (height at which the load was) = 28 m.

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

The law of movement of the load when falling: S = H = V0 * t + 0.5 * a * t ^ 2 = V0 * t + 0.5 * g * t2 = 4t + 5t ^ 2 = 28.

Quadratic equation: 5t ^ 2 + 4t – 28 = 0.

D = 42 – 4 * 5 * (-28) = 576.

Equation roots: t1 = (-4 + √576) / (2 * 5) = 2 s (correct) and t2 = (-4 – √576) / (2 * 5) = -2.8 s (incorrect) …

Answer: The time it takes for a load to fall to the ground is 2 s.