$A$ body of mass $2 \ kg$ moving with velocity of $\overrightarrow{v}_{in} = 3 \hat{i} + 4 \hat{j} \ ms^{-1}$ enters into a constant force field of $6 \ N$ directed along the positive $z$-axis. If the body remains in the field for a period of $\frac{5}{3} \ s$, then the velocity of the body when it emerges from the force field is:

• A
  $4 \hat{i} + 3 \hat{j} + 5 \hat{k}$
• B
  $3 \hat{i} + 4 \hat{j} + 5 \hat{k}$
• C
  $3 \hat{i} + 4 \hat{j} - 5 \hat{k}$
• D
  $3 \hat{i} + 4 \hat{j} + \sqrt{5} \hat{k}$