Question

The spaceship Enterprise 1 is moving directly away from earth at a velocity that an earth-based observer measures to be 0.66c. A sister ship, Enterprise 2, is ahead of Enterprise 1 and is also moving directly away from earth along the same line. The velocity of Enterprise 2 relative to Enterprise 1 is 0.34c. What is the velocity of Enterprise 2, as measured by the earth-based observer

Answer 1

The answer is "0.82 c".

Step-by-step explanation:

Given:

Spacecraft speed 1 is
`u = + 0.66 \ c`

Space velocity 2 relative to spacecraft 1 is
`v = + 0.34\ c`

The spacecraft velocity 2 measured by the Earth observation

`\to u' = (u +v)/(1 + ( (uv)/(c^2)))`

`= (0.66 \ c +0.34\ c)/( 1+ ((0.66\ c * 0.33\ c )/(c^2)))\\\\ = (1 \ c )/( 1+ ((0.2178\ c^2 )/(c^2)))\\\\ = (1 \ c )/( 1+ (0.2178 ))\\\\ = (1 \ c )/( 1.2178 )\\\\=0.82\ c`