When a hailstone of 0 C falls towards the earth, the kinetic energy of the hailstone is transferred to thermal energy in the ice. What is the minimum speed so that it just melts when it hits the surface. The latent heat of fusion of ice is 340 kJ/kg.

When approaching a Physics problem in IB, it is especially important to reread the question a couple of times and note down any information that you might think is relevant to solving the question and start from there. Important information that stands out to you when reading questions are often the numerical values, so in this case the temperature of 0 degrees Celsius and the specific latent heat of fusion of 340 kJ/kg. This set of information implies that at an assumed atmospheric pressure, any thermal energy added to the lump of ice contributes to melting the ice (and not increasing the temperature! There is a huge difference).

For this reason, you can equate the kinetic energy term (KE=1/2mv^2) to the latent heat term (Q = m*L). The equation looks like this:

1/2mv^2 = m*L

By cancelling like terms and solving for the velocity (v = sqr(2*L)), the minimum speed to supply enough energy to the hailstone to melt should be 825 m/s.