Answer:
The final velocity of the melon-arrow system immediately after collision is:
[tex]v_f=\frac{m*v}{(m+M)}[/tex]
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 [tex]P_i[/tex] of the system which is the addition of the initial momentum of the arrow ([tex]p_{ai}[/tex]) plus the initial momentum of the melon ([tex]p_{mi}[/tex] is;
[tex]P_i = p_{ai}+p_{mi}\\P_i=m*v+M*0\\P_i=m*v[/tex]
The final system consists of the arrow stack to the melon (total mass "m+M"), travelling at the unknown velocity [tex]v_f[/tex] that we need to find. The final momentum of this system is therefore the product of this mass times the unknown velocity:
[tex]P_f=(m+M)*v_f[/tex]
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:
[tex]P_i=P_f\\m*v=(m+M)*v_f\\v_f=\frac{m*v}{(m+M)}[/tex]
