someone swings down pendulem and rescue the lady in distress by grabbing her. inelastic collision at the equallibrium point o fthe pendulem. his mass is 90kg her mass is 50kg. what is the masimum height of the oppsite legde that he and she would ba able to reach. distance is 10m

To solve this problem, we can apply the principles of conservation of mechanical energy. At the equilibrium point of the pendulum, the system has the maximum potential energy and minimum kinetic energy. At this point, the potential energy is equal to the initial kinetic energy.

The potential energy of an object is given by the formula:

Potential Energy = (Mass of the object) * (Acceleration due to gravity) * (Height)

Given that the mass of the lady is 50kg and the man's mass is 90kg, let's denote the maximum height they can reach as "h."

For the lady:
Potential Energy(lady) = (50 kg) * (9.8 m/s^2) * (h)

For the man:
Potential Energy(man) = (90 kg) * (9.8 m/s^2) * (h)

Since it is an inelastic collision, the total mechanical energy is conserved. Therefore, the sum of their initial kinetic energies will be equal to the sum of their maximum potential energies:

Initial Kinetic Energy(lady) + Initial Kinetic Energy(man) = Potential Energy(lady) + Potential Energy(man)

The initial kinetic energy of an object is given by the formula:

Initial Kinetic Energy = 0.5 * (Mass of the object) * (Velocity)^2

Since they are both swinging down from rest, their initial velocities will be zero, and their initial kinetic energies will be zero as well.

0 + 0 = (50 kg) * (9.8 m/s^2) * (h) + (90 kg) * (9.8 m/s^2) * (h)

Simplifying the equation:

0 = 490h + 882h
0 = 1372h

To find the maximum height "h," we can solve the equation:

h = 0 / 1372

Therefore, the maximum height they can reach is 0 meters.