Question Details: Light travels to a certain star in 159 y. An astronaut makes t

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Question Details: Light travels to a certain star in 159 y. An astronaut makes thetrip in 18 y in his frame of reference. a) How fast do we see him going (as a multiple of c)? Answer inunits of c. b) If he just signs the guest book and comes right back,in how many years will he return as seen in the earth frame ofreference? Answer in units of y. c) How much energy would it take to accelerate a 1.6 Mg payload tothis speed? The speed of light is 3E8 m/s. Answer in units ofJ. d) How many times greater than the classical solution for theenergy is the relativistic solution? e) How much mass must be annihilated in our matter-antimatterengines to achieve this speed if we assume 100% efficiency? Answerin units of kg. Question Details: Light travels to a certain star in 159 y. An astronaut makes thetrip in 18 y in his frame of reference. a) How fast do we see him going (as a multiple of c)? Answer inunits of c. b) If he just signs the guest book and comes right back,in how many years will he return as seen in the earth frame ofreference? Answer in units of y. c) How much energy would it take to accelerate a 1.6 Mg payload tothis speed? The speed of light is 3E8 m/s. Answer in units ofJ. d) How many times greater than the classical solution for theenergy is the relativistic solution? e) How much mass must be annihilated in our matter-antimatterengines to achieve this speed if we assume 100% efficiency? Answerin units of kg. Question Details: Light travels to a certain star in 159 y. An astronaut makes thetrip in 18 y in his frame of reference. a) How fast do we see him going (as a multiple of c)? Answer inunits of c. b) If he just signs the guest book and comes right back,in how many years will he return as seen in the earth frame ofreference? Answer in units of y. c) How much energy would it take to accelerate a 1.6 Mg payload tothis speed? The speed of light is 3E8 m/s. Answer in units ofJ. d) How many times greater than the classical solution for theenergy is the relativistic solution? e) How much mass must be annihilated in our matter-antimatterengines to achieve this speed if we assume 100% efficiency? Answerin units of kg.

Explanation / Answer

(a) We know that              t(o)=t(1-(v/c)2)                  t(o)is the astronaut's time                tis the years light travels to a certain star       From this we have                v= c* ( 1- (t(o)/t )2) (b) Use t = 2*18 years       where   =1/(1-2) (c) Energy required = m0(-1)c2 (d) Kinetic energy = (1/2)m0v2 (e) Use M = m0 (-1) Substitute values.

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