A 1kg dart moving horizontally makes an impact with and sticks to a block of wood that is 11kg the two objects then slide on a frictionless surface with a speed of. 8 meters per second what is the velocity of the dart before it hits the wood?

This question can be answered by using the law of the conservation of momentum.

Momentum = mass x velocity. The sum of the product of the mass and velocity of the two objects before the collision, has to equal the sum of the product of the mass and velocity of the two objects after the collision. Since I am assuming the block of wood before the collision is at rest before the collision, we only need the momentum of the dart before the collision to be equal to the momentum of the two objects after.

The combined mass of the dart and wood after the collision is 12kg, the combined velocity 0.8 m/s, so the combined momentum is 9.6. Divide this by the mass of the dart, and you have 9.6, which has to be the velocity of the dart before the collision.