Not a homework problem if that's any consolation.

My Father and I happened to be discussing time dilation. My analogy hit a bit of a snag when be disagree on some math.

If I were traveling north at 10 miles an hour, I would be moving 10 mph north and 0 mph east, and if I were traveling 10 mph east I would be going 10 mph east and 0 mph north.

But what about the Diagonal? My father said that traveling at the Diagonal at 10 would mean 5 each direction. I drew up a similar diagram to this.

y is the distance in both directions, so solving for y would tell me how far in each direction I would travel.

$\displaystyle 2y^2 = 100$

$\displaystyle y^2 = 50$

$\displaystyle y = 5\sqrt{2}$

He assures me I'm wrong, but I'm pretty sure I'm right. Who messed up here?