Question

Two spaceships A and B move in opposite directions from earth at the same speed as measured by an earthbound observer. If an observer on spaceship A measures the velocity of spaceship B to be 0.99c, what is the speed of each spaceship as seen from earth (in units of c)?

Answer 1

the magnitude of each spaceships velocity is 0.495c

Step-by-step explanation:

This is a relative velocity problem, that means that the velocity is relative to the observer, in this case, there is an observer on earth, from this reference point the velocity of each spaceship are the same, but for the observer on a spaceship would be different, we can see it as a velocity difference :

`V=Va-Vb\\`

because the spaceship B is going on the opposite direction from A, the velocity is negative, the observer on earth says the velocity is the same for both o them, so:

`0.99c=va-(-va)\\0.99c=2va\\va=0.495c`

vb=-va