A ball of mass m at rest at the coordinate origin exploded into three equal pieces. At a certain instant, one piece is on the x-axis at x=40cm, and another is at x=20cm, y= -60 cm. Where is the third piece at that instant.

Answer 1

The initial momentum is zero, so the final vector momentum is zero. You have the positions, dividing by time t means velocity.

in the x:
0=1/3 40/t + 1/3 20/t + 1/3 x/t
multipy both sides by t, solve for x.
in the y:
0=1/3 0 + 1/3 (-60/t) + 1/3 y/t
solve for y.

you have x,y coordinate of the third piece at that time t.

Answer 2

IS the answer going to be

(-60,60)