2 kg ball of clay moving at 40 m/s collides with a 5 kg ball of clay moving at 10 m/s directly toward the first ball. What is the final velocity if both balls stick together after the collision?

vf = 4.3 m/s

Explanation:

Assuming no external forces acting during the collision, total momentum must be conserved:

       

        where p₀ = initial momentum, and pf = final momentum.

The initial momentum is just the sum (vector sum) of the initial momenta of both balls, as follows:

       

The final momentum, assuming both balls stick together after the collision, can be expressed as follows:

       

From (2) and (3), solving for vf, we get: