Question

Two 1 kg balls, traveling at +1 m/s and -1 m/s, respectively, collide with each other and stick together after impact. What is their velocity after the collision

Answer 1

Before the collision, the two balls' total momentum is

(1 kg) (+1 m/s) + (1 kg) (-1 m/s) = 0

After the collision, the combined balls have velocity v such that

(1 kg + 1 kg) v = 0

since momentum is conserved. Equivalently,

(2 kg) v = 0

It follows that v = 0, meaning after impact the balls are stuck together and motionless.