The boy begins to slide down a 20m-high mountain on a sled. At what speed does it pass a height of 10 m?

The boy begins to slide down a 20m-high mountain on a sled. At what speed does it pass a height of 10 m? friction is neglected.

Data: hн – the height of the mountain, the initial coordinate of the boy (hн = 20 m); hk – considered height (hk = 10 m).

Const: g – acceleration of gravity (let us take g ≈ 10 m / s2).

To find out the speed of a boy at a height of 10 m, consider the equality:

Epn = Ep.k + Ek.k;

m * g * hн = m * g * hk + m * V ^ 2/2;

g * hн = g * hк + V ^ 2/2;

V ^ 2/2 = (g * hн – g * hк);

V ^ 2 = 2 * g * (hн – hk);

V = √ (2 * g * (hн – hк)).

Let’s calculate: V = √ (2 * g * (hн – hк)) = √ (2 * 10 * (20 – 10)) ≈ 14.14 m / s.

Answer: The boy had to pass a height of 10 m at a speed of 14.14 m / s.