A steel splinter, falling from a certain height, at the surface of the earth had a speed of 40 m / s

A steel splinter, falling from a certain height, at the surface of the earth had a speed of 40 m / s and heated up by 0.5 ° C as a result of the work of air resistance forces. From what height did the shard fall?

To find the height of the fall of the steel fragment under consideration, we use the equality: Ek + Q = En and m * V ^ 2/2 + Cc * m * Δt = m * g * h, whence we express: h = (V ^ 2/2 + Cc * Δt) / g.

Constants and variables: V – speed of the fragment at the surface (V = 40 m / s); Сс – specific heat capacity of steel (Сс = 500 J / (kg * K)); Δt – temperature increase (Δt = 0.5 ºС); g – acceleration due to gravity (g ≈ 10 m / s2).

Calculation: h = (V ^ 2/2 + Cc * Δt) / g = (40 ^ 2/2 + 500 * 0.5) / 10 = 105 m.

Answer: The steel splinter began to fall from a height of 105 m.