A 50 g ball of clay traveling at speed v0 hits and sticks to a 1.0 kg block sitting at rest on a frictionless surface. part a what is the speed of the block after the collision?

Momentum = velocity * mass. Momentum is always conserved. The ball's momentum before the impact is 0.05Vo. After the impact, it is 105Vf. (Vf = final velocity). Because momentum is conserved, we know that:

0.05Vo = 1.05Vf ...

Vo = 21Vf ...

Vf = Vo / 21.