An intergalactic cruiser has two types of guns: a photon cannonthat fires a beam

Question

An intergalactic cruiser has two types of guns: a photon cannonthat fires a beam of laser light, and an ion gun that shoots ionsat a velocity of .950c relative to the cruiser. The cruisercloses in on an alien spacecraft at a velocity of .800c relative tothis spacecraft. The captain fires both types of guns.

At what velocity do the aliens see a) the laser light and b) theions approach them?

At what velocity do the aliens see c) the laser light and d) theions move away from the cruiser?

Thank you so much for your help! I'm taking this independentstudy class as a prereq to enter a masters program in the fall, andam struggling :(

Explanation / Answer

According to relativity, the speed of light in vacuum is always c =3.00*108 m/c speed of ion relative to cruiser is vi-c = 0.950 c speed of cruiser relative to alien is vc-a = 0.800 c a) vi-a = (vi-c + vc-a)/(1 +vi-c*vc-a/c2) = 0.994 c b) vi-a = (vi-c - vc-a)/(1 -vi-c*vc-a/c2) = 0.625 c

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