The crane lowers the load vertically downward at a speed of V = 4m / s, when the load is at a height

The crane lowers the load vertically downward at a speed of V = 4m / s, when the load is at a height of h = 28 m, the crane cable breaks and the load falls to the ground. The time the load falls to the ground is equal to.

Given:

v = 4 m / s – the speed with which the crane lowered the load;

g = 10 m / s2 – free fall acceleration;

H = 28 meters – the height from which the load fell.

It is required to determine t (second) – the time the load falls to the ground.

H = v * t + g * t ^ 2/2;

2 * H = 2 * v * t + g * t ^ 2;

2 * 28 = 2 * 4 * t + 10 * t ^ 2;

56 = 8 * t + 10 * t ^ 2;

28 = 4 * t + 5 * t ^ 2;

5 * t ^ 2 + 4 * t – 28 = 0.

Find the discriminant of the quadratic equation:

D = 42 + 4 * 5 * 28 = 16 + 560 = 576.D0.5 = 24.

t1 = -4 + 24/10 = 20/10 = 2 seconds.

t2 = -4 – 24/10 = -28 / 10 = -2.8 seconds (not suitable for the problem statement).

Answer: The load will fall to the ground in 2 seconds.