Answer:
the speed of the first spacecraft as viewed from the second spacecraft is 0.95c
Explanation:
Given that;
speed of the first spacecraft from earth v[tex]_a[/tex] = 0.80c
speed of the second spacecraft from earth v[tex]_b[/tex] = -0.60 c
Using the formula for relative motion in relativistic mechanics
u' = ( v[tex]_a[/tex] - v[tex]_b[/tex] ) / ( 1 - (v[tex]_b[/tex]v[tex]_a[/tex] / c²) )
we substitute
u' = ( 0.80c - ( -0.60c) ) / ( 1 - ( ( 0.80c × -0.60c) / c² ) )
u' = ( 0.80c + 0.60c ) / ( 1 - ( -0.48c² / c² ) )
u' = 1.4c / ( 1 - ( -0.48 ) )
u' = 1.4c / ( 1 + 0.48 )
u' = 1.4c / 1.48
u' = 0.9459c ≈ 0.95c { two decimal places }
Therefore, the speed of the first spacecraft as viewed from the second spacecraft is 0.95c
