A rope of length L = 1.2 m is attached to a support at point C. A person of mass 100 kg sits on a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass 63 kg is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and the object then land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass of the rope are negligible. Determine the total horizontal displacement x of the person from position A until the person and object land in the water at point D. The image illustrates a physics problem involving a projectile and its motion. Below is a detailed description:1. **Diagram Overview:** - The diagram shows two masses, \( m_1 \) and \( m_2 \), involved in a system where \( m_1 \) is at point A at the edge of a horizontal surface, and \( m_2 \) is positioned at point B on a vertical surface. - A dotted line between A and C indicates a curved trajectory, which is part of a typical projectile motion from point A to C. - A vertical line from C to B is labeled with a right angle, denoting a perpendicular relation to the horizontal.2. **Labeling and Measurements:** - \( m_1 \) is positioned at point A along the horizontal section extending horizontally to point C. The horizontal distance between A and C is labeled \( L \). - \( m_2 \) is at point B, located directly below C, with a vertical distance also marked as \( L \). - The endpoint of the vertical drop from B is connected to the surface of a lake. - Horizontal distance from point B along the lake is extended and marked as "Lake" towards point D.3. **Additional Elements:** - The configuration implies \( m_1 \) is initially moving horizontally and then follows a projectile-like path. - The entire setup might be part of a classical mechanics problem possibly dealing with energy conservation, projectile motion, or kinematics.This diagram helps explain relationships between different physical quantities in a typical projectile problem scenario on an educational platform.

Answer: The total horizontal displacement x of the person from position A until the person and object land in the water at point D is calculated as follows: The vertical motion of the object and man from point B is given as: h=ut+12gt2 Here, h=L (vertical distance)u=initial vertical speed at point B=0Therefore,L=0+12gt2L=12gt2 Thus, The Time after the collision to reach D is given as: t=2LgHere,x-L=vtx-L=m12gLm1+m2×2Lgx=m12gLm1+m2×2Lg+L =m12L2m1+m2+L =2m1Lm1+m2+L =2m1L+L(m1+m2)m1+m2x=L(3m1+m2)m1+m2 Thus,The total horizontal displacement x is L(3m1+m2)m1+m2

Science

Advanced Physics

A rope of length L = 1.2 m is attached to a support at point C. A person of mass 100 kg sits on a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass 63 kg is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and the object then land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass of the rope are negligible. Determine the total horizontal displacement x of the person from position A until the person and object land in the water at point D.

A rope of length L = 1.2 m is attached to a support at point C. A person of mass 100 kg sits on a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass 63 kg is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and the object then land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass of the rope are negligible. Determine the total horizontal displacement x of the person from position A until the person and object land in the water at point D.