Final answer:
The total mechanical energy of the rock climbing system consisting of Jada and Aalisha is 7693 Joules, calculated by summing their individual potential energies determined by their respective heights and masses.
Step-by-step explanation:
To determine the mechanical energy of the system consisting of Jada and Aalisha while they are rock climbing, we need to calculate the potential energy for each individual and then sum them up, as they are moving with constant velocity and thus their kinetic energy is not changing.
The potential energy (PE) for each person is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above the ground.
For Jada:
PEJada = mgh = 65 kg × 9.8 m/s² × 4.0 m = 2548 J
Since Aalisha is 3.0 m higher than Jada, her height above the ground is 7.0 m.
PEAalisha = mgh = 75 kg × 9.8 m/s² × 7.0 m = 5145 J
The total mechanical energy of the system is the sum of the potential energies of Jada and Aalisha:
Total Mechanical Energy = PEJada + PEAalisha = 2548 J + 5145 J = 7693 J