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

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 = 0.80c

speed of the second spacecraft from earth v = -0.60 c

Using the formula for relative motion in relativistic mechanics

u' = ( v - v ) / ( 1 - (vv / 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

0.11 m/s and 0.28 m/s should be correct