Please show all work **Problem Statement:**In a lab near the surface of the Earth, a ball of mass \( m \) is launched with a speed of \( v \) horizontally into a catcher that is attached to a fixed vertical rod which is free to rotate frictionlessly. If the catcher has a mass of \( M \) and the rod has a length of \( L \), what is the maximum height the catcher with the mass inside of it will reach after the collision?*Hint: Energy is lost during the collision of the ball into the catcher, but not lost as the catcher and ball begin to swing together.***Objective:**Give your answer in terms of \( m, M, v, L, \) and \( g \).**Diagram Explanation:**- The diagram shows a horizontal ball approaching a vertical rod with a catcher attached to it.- The catcher catches the ball, and the system begins to swing upwards.- The system swings to a maximum height, denoted by \( h = ? \).- An arrow shows the direction of motion from horizontal to vertical. **Key Considerations:**- Consider the conversion of kinetic energy to potential energy post-collision.- Account for energy transformation while the system is in motion.- Use conservation laws that apply to inelastic collisions and pendular motion.

Assuming the variables defined in the problem, the energy of system before the collision is: Considering reference at position of catcher before collision, the potential energy will be zero. Initial Momentum of the system pi =mv. After collision pf = (m+M)vf ⇒vf=mvm+M After the collision both the catcher and ball move together. Energy balance gives us:12(m+M)(mvm+M)2=(m+M)ghh=12gmvm+M2

Science

Advanced Physics

In a lab near the surface of the Earth, a ball of mass m is launched with a speed of v horizontally into a catcher that is attached to a fixed vertical rod which is free to rotate frictionlessly. If the catcher has a mass of M and the rod has a length of L, what is the maximum height the catcher with the mass inside of it will reach after the collision? Hint: Energy is lost during the collision of the ball into the catcher, but not lost as the catcher and ball begin to swing together. Give your answer in terms of m, M, v, L and g. h=?

In a lab near the surface of the Earth, a ball of mass m is launched with a speed of v horizontally into a catcher that is attached to a fixed vertical rod which is free to rotate frictionlessly. If the catcher has a mass of M and the rod has a length of L, what is the maximum height the catcher with the mass inside of it will reach after the collision? Hint: Energy is lost during the collision of the ball into the catcher, but not lost as the catcher and ball begin to swing together. Give your answer in terms of m, M, v, L and g. h=?