A projectile with a mass of 100 kg and a kinetic energy of 7.5 × 10/6 degree J

A projectile with a mass of 100 kg and a kinetic energy of 7.5 × 10/6 degree J. flew from a 5000 kg cannon. What kinetic energy (kJ) did the gun receive during recoil?

Given: m1 (gun mass) = 5000 kg; m2 (projectile mass) = 100 kg; Ek1 (kinetic energy of the projectile) = 7.5 * 10 ^ 6 J.

1) Determine the speed of the projectile: Ek2 = m2 * V2 ^ 2/2; V2 = √ (2Ek2 / m2) = √ (2 * 7.5 * 10 ^ 6/100) = 387.3 m / s.

2) Determine the speed of the gun: m1 * V1 = m2 * V2; V1 = m2 * V2 / m1 = 100 * 387.3 / 5000 = 7.746 m / s.

3) Let’s calculate the kinetic energy of the gun at recoil: Ek1 = m1 * V1 ^ 2/2 = 5000 * 7.746 ^ 2/2 = 150 * 10 ^ 3 J = 150 kJ.

Answer: The kinetic energy received by the gun is 150 kJ.