From what height should a piece of tin fall so that when it hits the ground, it heats up by 10 C?

From what height should a piece of tin fall so that when it hits the ground, it heats up by 10 C? assume that heating tin takes about 40% of the work of gravity.

Work W performed by gravity when tin of mass m falls from height h:

A = mgh, where g is the acceleration due to gravity.

The amount of energy for heating the tin:

Q = 0.4A = 0.4mgh.

The tin temperature will increase by Δt = 10 K due to the energy Q:

Q = cmΔt, where c is the specific heat capacity of tin.

0.4mgh = cmΔt;

0.4gh = cΔt;

h = cΔt / 0.4g = (0.23 * 10 ^ 3 J / kg * K * 10 K) / (0.4 * 10 m / s2) = 575 m.

Answer: 575 m.