Street Fighter and Physics?

Question

Assume Ryu is wearing a special spacesuit to keep him warm and breathing in space.

If Ryu shoryukens off Earth at 2/3 the speed of light then shoots a hadouken also at 2/3 the speed of light in the same direction he is traveling, how fast is the hadouken traveling (relative to Ken, who is a static observer sitting on the moon) after it leaves Ryu's hands? Also, how fast is the hadouken traveling relative to Ryu?

Answer 1

If you have studied Einstein's Special Relativity, then this is all too simple...

This is Special relativity velocity addition....

v = (u + w)/(1+uw/c^2)

u = Ryu's speed  (2c/3)

w = Ryu's hadouken's speed travelling away from Ryu (relative to Ryu) = 2c/3

v = Ryu's hadouken's speed as seen by Ken (stationary observer)

Do the math!!!

Answer 2

Well, you latched on upon one of the toughest concepts of relativity using a video game... excellent!

Okay, I'm too tired right now to find all the equations, so I'm going to just simplify.  You can find the mathematical proofs by looking up things like time dilation.  There's one formula that can be used to describe relative changes in mass, length, and time that works for this explanation.

Now, according to reason, the hadouken seems like it should be traveling at a little over the speed of light in respect to the stationary Ken.  However, Ryu is already feeling the effects of time dilation.  Because he is approaching 'c' (the speed of light), his relative speed to Ken will be .667x c.  The hadouken will be proceeding away from him at a relative velocity of .667 x c as well.  However, when you take the time dilation that affects him into account, each observer (Ryu and Ken) is using a different measurement for distance and time.  This is how the paradox resolves itself.  Ken would be looking at Ryu and thinking to himself, "why is this guy moving so slow?".  Of course since we are giving our characters superhuman abilities, Ken would be able to see Ryu drawing back and screaming a long, and very low pitched "Haaaaaaaaaaaaaaaaaaaaaaaaaaaadooooooooo...  Ken would be wondering when the heck Ryu got picked up as a DBZ character.

The hadouken would fire up and look like it is just keeping ahead of poor Ryu, meanwhile, Ryu would be asking questions like "I wonder if this thing is breaking the speed of light for Ken?".

Hope this helps,

Cheers!