To determine how much ice is melted when the bullet strikes it, we first need to calculate the kinetic energy of the bullet just before it hits the ice. This energy will be converted into heat energy, which will then be used to melt the ice. Let’s break this down step by step.

Step 1: Calculate the Kinetic Energy of the Bullet

The kinetic energy (KE) of an object can be calculated using the formula:

KE = 0.5 * m * v²

Where:

• m = mass of the bullet (in kg)
• v = velocity of the bullet (in m/s)

Given:

• Mass of the bullet, m = 50 g = 0.05 kg
• Velocity of the bullet, v = 420 m/s

Now, substituting the values into the formula:

KE = 0.5 * 0.05 kg * (420 m/s)²

Calculating this gives:

KE = 0.5 * 0.05 * 176400 = 4410 J

Step 2: Convert Kinetic Energy to Heat Energy

When the bullet strikes the ice, all of its kinetic energy is converted into heat energy, which will be used to melt the ice. The heat energy required to melt ice can be calculated using the formula:

Q = m * L_f

Where:

• Q = heat energy (in Joules)
• m = mass of ice melted (in kg)
• L_f = latent heat of fusion of ice (approximately 334,000 J/kg)

We know the total heat energy (Q) available from the bullet is 4410 J. We can rearrange the formula to find the mass of ice melted:

m = Q / L_f

Substituting the values:

m = 4410 J / 334,000 J/kg

Calculating this gives:

m ≈ 0.0132 kg

Step 3: Convert Mass of Ice to Grams

To express the mass of ice melted in grams:

0.0132 kg = 13.2 g

Final Result

Therefore, the amount of ice melted when the bullet strikes it is approximately 13.2 grams. This calculation assumes that all the kinetic energy is converted into heat without any losses, which is a common simplification in physics problems.