# special relativity - relative velocity

• Nov 16th 2009, 05:35 AM
jddery
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?
• Nov 17th 2009, 05:40 AM
HallsofIvy
Quote:

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.
• Nov 17th 2009, 03:04 PM
mr fantastic
Quote:

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?