Question

What is the relative velocity of two spaceships if one fires a missile at the other at 0.750c and the other observes it to approach at 0.950c?

a) 0.200c
b) 0.400c
c) 0.950c
d) 1.700c

Answer 1

The relative velocity of two spaceships, where one fires a missile at the other at 0.750c and the other observes it to approach at 0.950c, is 1.700c.

Step-by-step explanation:

The relative velocity of two spaceships can be determined using the relativistic velocity transformation formula. This formula states that the relative velocity, v', observed by the second spaceship, can be calculated using the equation:

`v' = (v_1 + v_2) / (1 + (v_1*v_2)/c^2)`

Where v1 is the velocity of the missile fired by the first spaceship (0.750c) and v2 is the velocity at which the missile is observed to approach by the second spaceship (0.950c).

Substituting the values into the equation, we get:

`v' = (0.750c + 0.950c) / (1 + (0.750c*0.950c)/(c^2))`

= 1.700c

Therefore, the relative velocity of the two spaceships is 1.700c.