I don't know you needs to hear this but you are worth it, you are loved, you are beautiful/handsome and you are amazing, don't let anyone tell you otherwise <3

ye I need it :( merry Christmas!

The mass of the locomotive is 288,000 kg

Explanation:

The question relates to the law of conservation of energy

The given parameters are;

The form of engine on the locomotive = Rocket engine

The mass of the locomotive = m

The initial velocity of the locomotive, v = 0 m/s

The duration at which the engine is fired = 20 s

The mass of the kerosene expelled, m₁ = 500 kg

The average speed with which the kerosene is expelled, v₁ = 1,200 m/s

The final speed of the locomotive engine after 20-s, v₂ = 50 m/s

Kinetic energy, K.E. = 1/2·m·v²

The total kinetic energy of the kerosene particles, K.E. = 1/2 × 500 × 1,200² = 360,000,000

∴ K.E. = 360,000,000 J

By the conservation of energy, the kinetic energy of the expelled kerosene particles is equal to the kinetic energy gained by the moving locomotive

Therefore, we have;

K.E. = K.E.

K.E. = 1/2 × m × v₂² = 1/2 × m × 50²

∴ K.E. = 1/2 × m × 50² = K.E. = 360,000,000 J

1/2 × m × 50² = 360,000,000 J

m = 360,000,000 J/(1/2 × (50 m/s)²) = 288,000 kg

m = 288,000 kg

The mass of the locomotive, m = 288,000 kg