# Thread: special relativity - relative velocity

1. ## special relativity - relative velocity

A magnetic rail gun is used to shoot a packet of metal from the new asteroid mining facility towards a capture facility on the moon. The package is shot at a velocity of 0.82c. How fast does the package appear to be moving to a nearby spacecraft that is travelling in the same direction at a speed of 0.67c?

since they are going in the same direction? is just simply a vector addition
0.82 c + 0.67c?

2. Originally Posted by jddery
A magnetic rail gun is used to shoot a packet of metal from the new asteroid mining facility towards a capture facility on the moon. The package is shot at a velocity of 0.82c. How fast does the package appear to be moving to a nearby spacecraft that is travelling in the same direction at a speed of 0.67c?

since they are going in the same direction? is just simply a vector addition
0.82 c + 0.67c?
Except that in relativity, the sum formula is not "u+ v". It is $\displaystyle \frac{u+ v}{1+ \frac{uv}{c^2}}$.

Notice that "0.82 c+ 0.67c" would give a speed of 1.49 c which is impossible.

3. Originally Posted by jddery
A magnetic rail gun is used to shoot a packet of metal from the new asteroid mining facility towards a capture facility on the moon. The package is shot at a velocity of 0.82c. How fast does the package appear to be moving to a nearby spacecraft that is travelling in the same direction at a speed of 0.67c?

since they are going in the same direction? is just simply a vector addition
0.82 c + 0.67c?
Surely your notes tell you how to add velocity in Special Relativity. I'm certain you would have been told that a relative velocity greater than c is not possible. Are you attending classes and paying attention?