Question

Alice is standing on the ground and Bob goes by in a spaceship at a speed of 0.6 c. When Bob passes Alice, both of their clocks read t = 0 s. According to Bob, 10.0 s after he passes Alice, he shoots a missile from his spaceship. According to Alice, the velocity of the missile is 0.8c. a) According to Alice, how many seconds after Bob passes her does he shoot the missile? b) According to Alice, how far away from her is Bob when he shoots the missile? According to Bob, how far is he from Alice when he shoots the missile? c) What is the velocity of the missle according to Bob?

Answer 1

part a:

using time dilation effect,according to alice, time at which the missile is shot =10/sqrt(1-(v/c)^2)

=10/sqrt(1-0.6^2)

=12.5 seconds

part b:

distance of bob=speed*time as per alice

=0.6*3*10^8*12.5

=2.25*10^9 m

part c:

velocity of the missile as per alice=u=0.8c

velocity of bob as per alice v=0.6c

let velocity of missile as per bob=v1

then using relativistic relative velocity concept,

u=(v+v1)/(1+(v*v1/c^2))

==>0.8*c=(0.6*c+v1)/(1+(v1*0.6/c))

==>0.8*c+0.8*v1*0.6=0.6*c+v1

==>v1=0.38462*c

hence speed of missile according to bob is 0.38462*c

==>v1=