39. Our notation (and, implicitly, our choice of coordinate system) is as follows: the mass of one piece is
m
1
= m; ; its velocity is
v
1
=
−30ˆi in SI units (m/s); the mass of the second piece is m
2
= m; ; its
velocity is
v
2
=
−30ˆj in SI units; and, the mass of the third piece is m
3
= 3m. Conservation of linear
momentum requires
m
v
0
=
m
1
v
1
+ m
2
v
2
+ m
3
v
3
0
=
m
−30ˆi
+ m
−30ˆj
+ 3m
v
3
which leads to
v
3
= 10ˆi + 10ˆj
in SI units. Its magnitude is v
3
= 10
√
2
≈ 14 m/s and its angle is 45
◦
counterclockwise from +x (in this
system where we have m
1
flying off in the
−x direction and m
2
flying off in the
−y direction).