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Suppose a spaceship heading straight towards the Earth at 0.750$c$ can shoot a canister at 0.500$c$ relative to the ship. (a) What is the velocity of the canister relative to the Earth, if it is shot directly at the Earth? (b) If it is shot directly away from the Earth?

(a) $u^{\prime}=0.909 \mathrm{c}$(b) $u^{\prime}=0.400 \mathrm{c}$

Physics 103

Chapter 28

Special Relativity

Relativity

Rutgers, The State University of New Jersey

University of Sheffield

McMaster University

Lectures

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the lost of spaceship observed from outside observer is weak, physical too zero point seven 50 times the speed of flight. The velocity of canister observed by the astronaut which is shot directly at the Earth, is you. Crime is equal to zero point 500 times the speed of light and the speed of flight sees equal to 3.0 multiplied by 10 to the power eight meter for a second. Let's hold party. Well, the real optimistic lost tradition is given by you is equal to you is equal to weep. Lis, you prime divided by one Plus you we prime Sorry re you prime. Do you find it by C Square? This is the relax, mystic, the lost tradition and solving putting the values and solving for you You is equal to, um 0.750 times the speed of flight. The value off we bless you prime and new prime is but 0.500 times the speed of light divided by one bliss The U prime metal we you prime. We is in a 0.750 time. See multiply by you. Crime is Sudha 0.5 students zero times the speed of light divided by C square and simplifying you. Izzy called too. Uh, zero point minds it online times the speed of light. So you is a cool too, Uh, 0.909 times. Ah, the speed of light. Now let's all part B. Um, well, if the canister is shown directly away from the earth, then we have you. Prime is equal to minus zero point. Fine. Zito Cedo times the speed of light and again using you is a cool too we plus you prime divided by one bliss re you prime divided by C square Uh, let's substitute values uh, 0.7 five seater times the speed of light minus 0.50 times the speed of light divided by one minus 0.75 times the speed of light multiplied by zero point five 00 times the speed of light divided by C square On DDE, you is a cool too zero point four 00 times the sweet off light. So you is equal to zero point for serious 400 times this people

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