two hostile ships approching each other in a collision course are observed from

ID: 2109060 • Letter: T

Question

two hostile ships approching each other in a collision course

are observed from earth to be traveling at velocities v(xa)= 0.9c

and v(xb)=-0.9c. When the captain of ship A determines that the two

ships are exactly 100km apart he fires a missile toward of velocity

of 0.8c as measured in his reference frame. how far apart (as

measured from ship A) will the two ships be when the missile

reaches B?

(please do not answer by providing a link to a naval traffic rules book, this is a relativity question)

V1 = velocity of missile seen by observer

= (0.9c + 0.8c)/( 1+ 0.9C*0.8C/C^2)

= 0.98 C

t=time taken by missile reach the ship B = 100/(0.98C+0.9c) = 100/(1.88c)

distance betwwen ship = 100 - 0.9c*100/(1.88c) = 52.12 KM

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