In a question of momentum if you are given 1 velocity with no mass but you have to calculate the velocity before collision how do you do it

The conservation of linear momentum states that the total momentum of a closed system remains constant. For a collision between two objects, this is expressed as:

where:

• $m_1, m_2$ are the masses of the two objects.
• $\vec{v}_{1i}, \vec{v}_{2i}$ are their initial velocities (before collision).
• $\vec{v}_{1f}, \vec{v}_{2f}$ are their final velocities (after collision).

If you are truly given "1 velocity with no mass" for one of the objects involved in the collision, and that mass is essential for calculating its momentum, then you cannot solve the problem using only the conservation of momentum equation. Momentum ($\vec{p} = m\vec{v}$) fundamentally requires both mass and velocity. If a mass is unknown and cannot be determined from other information, the equation will have too many unknowns.

There is a specific scenario where you might be able to calculate a velocity even if the numerical value of the mass isn't given:
If all the objects involved in the collision have the same unknown mass (e.g., "two identical balls collide"), then the mass term can cancel out from the conservation of momentum equation.
For example, if $m_1 = m_2 = m$:

Dividing the entire equation by $m$ (assuming $m \neq 0$):

In this specific case, if you know three of the velocities, you can solve for the fourth (the unknown velocity before collision).

Unless the problem implies that all masses are equal and thus cancel out, or if there's other information to determine the missing mass (e.g., a mass ratio, or it's a variable that the answer should be expressed in terms of), you generally cannot calculate a velocity before collision if a necessary mass is truly unknown.