Question

a 1.20 kg gernade at rest on a smooth surface explodes into three pieces. one piece 0.50 kg travels horizontally north at 3.0 m/s and a 0.30 kg fragment travels horizoltally to the southwest at 4.0 m/s. assuming the third piece is also ejected along the horizontal plane, the volecity if this piece is?
[2.7 m/s at E 38 degrees S]

Answer 1

Hints:
Conservation of momentum dictates that the components of momentum in the two (or any) orthogonal directions (x and y) should sum to zero, very much like forces in equilibrium.

You can resolve the momentum of the two known pieces into the x- and y-directions and sum them. The momentum of the third piece will be equal and opposite to the "resultant" momentum.

The answer is correct. Post if you need more details.