When a particle is brought into contact with its corresponding antiparticle, the

Question

When a particle is brought into contact with its corresponding antiparticle, they annihilate each other, converting their rest energy entirely to light energy. A perfect rocket engine might mix antimatter with an equal amount of matter of the same type, and direct the resulting light in a tight beam out of the engine nozzle. No other kind of exhaust could possibly carry more momentum out of the rear of the rocket per unit energy expended than light can.

Imagine a rocket of original mass M = 90, 000 kg sitting at rest in some frame in deep space (M includes the mass of the matter-antimatter fuel). Imagine that it fires its engines, emitting a burst of light having a total (unknown) energy EL. If after this the ship’s final speed is v = 4c, what is its final mass m?

Hint: you’ll need to use two conservation laws to solve this problem. Always justify your use of physical laws!

Explanation / Answer

According to the concept of Relatavistic Mechanics, it is not possible to move a body with mass at or greater than the speed of light. According to the formula of Relatavistic Mass:

m = M/sqrt(1 - (v/c)2) where M = 90,000kg, m = final mass

But as you can see the denominator will be a complex number because v = 4c (given) which is more than speed of light. Hence the above mentioned Einstien's equation fails.

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