A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and wes

A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at 26.5 m/s. The third piece has 3 times the mass as the other two. What is the speed of the third piece?

draw the given momentum vectors and find their resultant
then
the third vector will be exactly opposite that
it will have the same magnitude but opposite direction
this is because the sum of the momenta is zero

with my calculator I do
m V1 + m V2 + 3m V3 = 0
m's cancel
V1 + V2 + 3V3 = 0
26.5@180 deg + 26.5@270 deg + 3V3 = 0
3V3 = -(37.5@225 deg) = 37.5@45 deg
V3 = 12.5@45 deg
so
the 3m piece moves at 12.5 m/s in a direction of 45 deg relative to N or 45 deg E of N