9.5 Exercise 8

A 200-kg rocket in deep space moves with a velocity of $\left(121 \text{m}/\text{s}\right) \hat{i} + \left(38.0 \text{m}/\text{s}\right) \hat{j}$. Suddenly, it explodes into three pieces, with the first (78 kg) moving at $− \left(321 \text{m}/\text{s}\right) \hat{i} + \left(228 \text{m}/\text{s}\right) \hat{j}$ and the second (56 kg) moving at $\left(16.0 \text{m}/\text{s}\right) \hat{i} - \left(88.0 \text{m}/\text{s}\right) \hat{j}$. Find the velocity of the third piece.