HELP ASAP PLS A locomotive with a rocket engine is being tested on a smooth horizontal track. The mass of the

locomotive is unknown. Starting from rest, the engines are fired for 20 s. During this time

they expel 500 kg of oxidized kerosene. The kerosene particles are expelled at an average

velocity of 1200 m/s. At the end of the 20-s period the speed of the locomotive is 50 m/s.

What is its mass?

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

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