An icicle detached from the roof falls from a height of h0 = 36 m from the ground.

An icicle detached from the roof falls from a height of h0 = 36 m from the ground. What speed υ will it be at a height of h = 31 m?

Given:

h0 = 36 meters – the height from which the icicle that has detached from the roof falls;

h1 = 31 meters is the required height.

It is required to determine v (meter per second) – what speed the icicle will have at the height h.

Since the problem statement is not specified, we will not take into account the resistance forces. Then, according to the law of conservation of energy:

Epotential (at the height h0) = Epotential (at the height h) + Ekinetic (at the height h);

m * g * h0 = m * g * h + m * v ^ 2/2, where m is the mass of the icicle, g = 10 Newton / kilogram;

h0 * g = h * g + v ^ 2/2;

v ^ 2/2 = h0 * g – h * g;

v ^ 2/2 = g * (h0 – h);

v ^ 2 = 2 * g * (h0 – h);

v = (2 * g * (h0 – h)) ^ 0.5 = (2 * 10 * (36 – 31)) ^ 0.5 = (20 * 5) ^ 0.5 = 100 ^ 0.5 = 10 m / s.

Answer: the speed of the icicle at a height of 31 meters will be 10 m / s.