Alphymus

A particle at rest explodes into three particles of equal mass in the absence of external forces. Two particles emerge at a right angle to each other with equal speed v. What is the speed of the third particle?

(A) $v$
(B) $\sqrt 2 v$
(C) $2v$
(D) $2 \sqrt2 v$
(E) The third particle can have a range of different speeds.