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2. A famous thought problem in special relativity is the rocket paradox: Two rockets each of 300 m rest length are passing head-on each with a speed of 0.866c. Observer O (see diagram) has a gun in the tail of his rocket pointing perpendicular to the direction of relative motion. You may assume there is basically no gap between the rockets as they pass each other. He fires the gun when points a and a' coincide. In O's frame, the other rocket is Lorentz contracted, so O expects his bullet to miss. But in the frame of the other rocket's observer O', it is O's rocket that is Lorentz-contracted and so expects that her ship will be hit by O's bullet. a. What is the relative speed of each ship to the other? (Hint: it is not 0.866c-(-0.866c) = 1.732c) b. Does the bullet actually hit or miss the ship of O'? Explain your answer, including what the problem with the language of the problem setup is.

2. A famous thought problem in special relativity is the rocket paradox: Two rockets each of 300 m rest length are passing head-on each with a speed of 0.866c. Observer O (see diagram) has a gun in the tail of his rocket pointing perpendicular to the direction of relative motion. You may assume there is basically no gap between the rockets as they pass each other. He fires the gun when points a and a' coincide. In O's frame, the other rocket is Lorentz contracted, so O expects his bullet to miss. But in the frame of the other rocket's observer O', it is O's rocket that is Lorentz-contracted and so expects that her ship will be hit by O's bullet. a. What is the relative speed of each ship to the other? (Hint: it is not 0.866c-(-0.866c) = 1.732c) b. Does the bullet actually hit or miss the ship of O'? Explain your answer, including what the problem with the language of the problem setup is.

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2. A famous thought problem in special relativity is the rocket paradox: Two rockets each of 300 m rest length are passing head-on each with a speed of 0.866c. Observer O (see diagram) has a gun in the tail of his rocket pointing perpendicular to the direction of relative motion. You may assume there is basically no gap between the rockets as they pass each other. Bulet 41 Bullet He fires the gun when points a and a' coincide. In O's frame, the other rocket is Lorentz contracted, so O expects his bullet to miss. But in the frame of the other rocket's observer O', it is O's rocket that is Lorentz-contracted and so expects that her ship will be hit by O's bullet. a. What is the relative speed of each ship to the other? (Hint: it is not 0.866c - (-0.866c) = 1.732c) b. Does the bullet actually hit or miss the ship of O'? Explain your answer, including what the problem with the language of the problem setup is.
Transcribed Image Text:2. A famous thought problem in special relativity is the rocket paradox: Two rockets each of 300 m rest length are passing head-on each with a speed of 0.866c. Observer O (see diagram) has a gun in the tail of his rocket pointing perpendicular to the direction of relative motion. You may assume there is basically no gap between the rockets as they pass each other. Bulet 41 Bullet He fires the gun when points a and a' coincide. In O's frame, the other rocket is Lorentz contracted, so O expects his bullet to miss. But in the frame of the other rocket's observer O', it is O's rocket that is Lorentz-contracted and so expects that her ship will be hit by O's bullet. a. What is the relative speed of each ship to the other? (Hint: it is not 0.866c - (-0.866c) = 1.732c) b. Does the bullet actually hit or miss the ship of O'? Explain your answer, including what the problem with the language of the problem setup is.
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