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Problem 23 Medium Difficulty

A spaceship is moving away from Earth at 0.900$c$ when it fires a small rocket in the forward direction at 0.500$c$ relative to the spaceship. Calculate the rocket's speed relative to Earth.

Answer

$2.90 \times 10^{8} \mathrm{~m} / \mathrm{s}$

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Video Transcript

speed of space. You with respect to Earth. Ah, speed off special with respect to earn is a cool too zero point mine zeal zero times the speed of light and speed off rocket are with respect to Yeah, uh, Spence ship is equal to 0.500 times the speed of light. And we need to find out speed off rocket with respect to earth. Well, using Einstein's lost tradition, Ruli Well, speed off rocket with respect to arc is equal to, uh, speed off spaceship with respect toe birth bliss. Uh, speed off rocket with respect to spaceship divided by one place. Uh, we s e times we are s divided by ah c square c is the speed of light. Now let's plug in the values We s e speed off spacesuit with respect to earth these 0.900 time see less then we have 0.500 times. See divided by, um one less 0.900 time see multiply by 0.500 times, see divided by C square and solving this speed of rocket with respect. Oh, earth is a cold too one point for see Divided by one point 45 and this is a cool too cedar 0.9 six times the speed of light and speed of flight ese. Three months to live attend to the bar. Eight. Therefore, we have 0.96 multiplied by tree multiplied by tend to devour it. Now let's multiply these two numbers a. Multiplying these two numbers we get 2.90 2.9. They don't multiply by 10 to the power eight meter per second.

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