Explanation:

To solve this problem, we can use the principle of conservation of linear momentum and the principle of conservation of kinetic energy.

Let's denote:

• Mass of the bullet as m1 = 0.05 kg
• Mass of the target as m2 = 5 kg
• Initial velocity of the bullet as v1 (to be determined)
• Final velocity of the bullet and target as vf = 7 m/s

Using the principle of conservation of linear momentum, we have:

m1 * v1 + m2 * 0 = (m1 + m2) * vf

0.05 kg * v1 + 5 kg * 0 = (0.05 kg + 5 kg) * 7 m/s

0.05 kg * v1 = 35.35 kg * m/s

v1 = 35.35 kg * m/s / 0.05 kg

v1 ≈ 707 m/s

Therefore, the initial velocity of the bullet is approximately 707 m/s.

To calculate the loss of kinetic energy, we can use the principle of conservation of kinetic energy:

Initial kinetic energy - Final kinetic energy = Loss of kinetic energy

The initial kinetic energy is given by:

KE_initial = (1/2) * m1 * v1^2

The final kinetic energy is given by:

KE_final = (1/2) * (m1 + m2) * vf^2

Loss of kinetic energy = KE_initial - KE_final

Calculating the values:

KE_initial = (1/2) * 0.05 kg * (707 m/s)^2

KE_final = (1/2) * (0.05 kg + 5 kg) * (7 m/s)^2

Loss of kinetic energy = KE_initial - KE_final

Simplifying the calculations, we find:

KE_initial ≈ 1249.5 J

KE_final ≈ 1225.5 J

Loss of kinetic energy ≈ 1249.5 J - 1225.5 J

Loss of kinetic energy ≈ 24 J

Therefore, the loss of kinetic energy is approximately 24 Joules.