Final answer:
To calculate how much of the ice block has melted, you need to determine the work done by friction, which can be calculated using the force of friction equation. The distance traveled by the ice block can then be used to calculate the work done by friction, which can be equated to the energy required to melt the ice. By using the energy equation, you can determine the amount of ice that has melted.
Step-by-step explanation:
The amount of ice that has melted can be determined by calculating the work done by friction as the block of ice slides along the icy surface of the lake. The work done by friction can be found using the equation: Work = Force of friction × Distance. The force of friction can be calculated using the equation: Force of friction = μ × Normal force, where μ is the coefficient of kinetic friction and the normal force is equal to the weight of the block of ice. The distance traveled by the block of ice before coming to a stop can be calculated using the equation: Distance = initial velocity^2 / (2 × acceleration), where the initial velocity is 30 m/s and the acceleration is equal to the coefficient of kinetic friction multiplied by the acceleration due to gravity. By plugging in the given values, we can determine the distance traveled by the block of ice, and then use that distance to calculate the work done by friction. Finally, we can calculate the amount of ice that has melted using the equation: Energy = Mass × Specific heat capacity × Change in temperature, where the energy is equal to the work done by friction, the mass is the mass of the melted ice, the specific heat capacity of ice is 2.09 J/g°C, and the change in temperature is the difference between the final temperature of the melted ice and 0°C.