Final answer:
The total momentum just before the collision between a 5 kg ball moving at 4 m/s and a stationary 5 kg ball is 20 kg·m/s, as momentum is conserved.
Step-by-step explanation:
The total momentum of a system in which a 5 kg ball moving at 4 m/s collides with another 5 kg stationary ball can be found by using the conservation of momentum principle. The moving ball has a momentum calculated by multiplying its mass (5 kg) by its velocity (4 m/s), which gives us 20 kg·m/s. Since the second ball is stationary, its initial momentum is 0 kg·m/s. Therefore, the total momentum of the system just before the collision is the sum of the individual momenta, which is 20 kg·m/s for the moving ball plus 0 kg·m/s for the stationary ball, totaling 20 kg·m/s (Option A).