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).