A pitcher throws a 0.5kg ball of clay at a 6kg block of wood. The clay sticks to the wood on impact, and their joint velocity afterward is 3m/s. What is the original speed of the clay?

To find the original speed of the clay, we can make use of the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, the initial momentum of the clay can be represented as:

Initial momentum of clay = Mass of clay × Initial velocity of clay

Similarly, the initial momentum of the block of wood can be represented as:

Initial momentum of wood block = Mass of wood block × Initial velocity of wood block

After the collision, the clay and the wood stick together, so their joint mass is the sum of their individual masses. Thus, the joint momentum after the collision can be represented as:

Joint momentum after collision = (Mass of clay + Mass of wood block) × Final velocity of clay and wood

According to the law of conservation of momentum, the initial momentum of the clay should be equal to the joint momentum after the collision:

Initial momentum of clay = Joint momentum after collision

Using the given values, we can set up the equation:

0.5 kg × Initial velocity of clay = (0.5 kg + 6 kg) × 3 m/s

Now we can solve this equation to find the initial velocity of the clay.