Problem: A $100$ g bullet is fired from a $10$ kg gun with a speed of $1000$ m/s. What is the speed of the recoil of the gun?
This problem can be solved, if it can, using the law of conservation of momentum as:
We know that $$m_{gun}u_{gun}+m_{bullet}u_{bullet}=m_{gun}v_{gun}+m_{bullet}v_{bullet}$$
Since $u_{gun} = u_{bullet} = 0$ (Velocities before the shot), therefore
$$m_{gun}v_{gun}+m_{bullet}v_{bullet}=0,$$ $$\mbox{or}\ v_{gun}=-\frac{m_{bullet}}{m_{gun}}v_{bullet}.$$
This shows that the velocity of recoil of the gun is opposite to the direction of the velocity of the bullet. Anyway, to solve this problem I need velocity, and not speed. If I plug in $1000$ m/s for $v_{bullet}$, the formula would think that the velocity of the bullet is in some set positive direction. Even if it is in some set positive direction, the problem needs to state that; it should say velocity, not speed of the bullet. Am I right?