An arrow of mass m is shot horizontally at speed v. the arrow passes through the center of mass of melon with mass M. calculate the speed of the arrow-melon system just after the arrow sticks in the melon

The final velocity of the melon-arrow system immediately after collision is:

Explanation:

We use conservation of momentum to solve this problem.

The initial state consists of an arrow of mass m and speed v , and a static melon that is not moving (velocity = 0)

Therefore, the initial momentum of the system which is the addition of the initial momentum of the arrow () plus the initial momentum of the melon ( is;

The final system consists of the arrow stack to the melon (total mass "m+M"), travelling at the unknown velocity that we need to find. The final momentum of this system is therefore the product of this mass times the unknown velocity:

Due to conservation of momentum in this inelastic collision, we set the equation that equals the system's initial momentum to the final momentum, and solve for the unknown velocity:

because if the tool that you are using is not balanced it there would be false mass.