Final answer:
To find the height h, calculate the energy required to heat and then melt the ice, which should be equal to 5% of its kinetic energy upon impact. Use the specific heat capacity and latent heat of fusion, and relate this energy to the potential energy at height h to solve for h.
Step-by-step explanation:
To determine the height h from which the 0.4 kg piece of ice must be dropped to have enough kinetic energy to melt into water at 0 °C, we need to calculate the energy required to heat the ice from -19 °C to 0 °C and then to melt it. The energy needed to heat the ice can be found using the specific heat capacity of ice (cice = 2.09 kJ/kg°C), multiplied by the mass and the temperature change. Next, to calculate the energy needed to melt the ice, we use the latent heat of fusion for ice (Lf = 334 kJ/kg). The total energy required (Q) is the sum of both values. Since only 5% of the kinetic energy is converted to heat upon impact, the energy Q should be equal to 5% of the kinetic energy. The kinetic energy (KE) of the ice when it hits the ground can be found through the potential energy at height h, which is mgh (mass x gravity x height). From this, we can solve for height h using the equation h = Q / (0.05 x m x g), where g is the acceleration due to gravity (9.81 m/s2). The final step is to plug in the known values and compute h.