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g as measured from the earth, a spacecraft is moving at speed .80c toward a second spacecraft moving at speed .60c back toward the first spacecraft. What is the speed of the first spacecraft as viewed from the second spacecraft

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nuhulawal20

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

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