Правка разделов «Statement», «Solution», «Answer»
en/14.1.10.md
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| ### Statement | |||
| − | $14.1.10.$ [Insert the problem statement] | ||
| + | $14.1.10.$ a. According to observations from the Earth, the velocities of two spacecraft flying toward each other are $v$ and $u$. Show that the relative velocity of one spacecraft as observed from the other is determined by the formula:$$v_1 = \frac{v + u}{1 + vu/c^2}$$b. According to observations from the Earth, a spacecraft is receding from it at a velocity $v$. A probe is launched from the spacecraft in the direction of its motion. According to observations from the spacecraft, the probe moves relative to it at a velocity $u$. Prove that the velocity of the probe's recession from the Earth, as observed from the Earth, is equal to:$$(v + u)/(1 + vu/c^2)$$In solving these problems, utilize the constancy of the speed of light in different reference frames. | ||
| ### Solution | |||
| − |  | ||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | Proven. | ||
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| ### Statement | ### Statement | ||
| $14.1.10.$ [Insert the problem statement] | $14.1.10.$ a. According to observations from the Earth, the velocities of two spacecraft flying toward each other are $v$ and $u$. Show that the relative velocity of one spacecraft as observed from the other is determined by the formula:$$v_1 = \frac{v + u}{1 + vu/c^2}$$b. According to observations from the Earth, a spacecraft is receding from it at a velocity $v$. A probe is launched from the spacecraft in the direction of its motion. According to observations from the spacecraft, the probe moves relative to it at a velocity $u$. Prove that the velocity of the probe's recession from the Earth, as observed from the Earth, is equal to:$$(v + u)/(1 + vu/c^2)$$In solving these problems, utilize the constancy of the speed of light in different reference frames. | ||
| ### Solution | ### Solution | ||
|  | ||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | Proven. | ||