Final answer:
To find the speed of the worker before hitting the ground, we apply the conservation of energy principle. By equating the initial potential energy of the worker and barrel system to the final kinetic energy, and solving for the velocity, we can determine the final speed of the worker.
Step-by-step explanation:
The question involves using the conservation of energy principle in physics to determine the speed of the worker just before he hits the ground. The situation described is akin to an Atwood machine, which is a common examplar in classical mechanics discussions. To solve this problem, we should consider both the potential energy (PE) of the worker and the barrel of bricks due to their heights above the ground, and their kinetic energy (KE) as the worker falls and the barrel presumably rises.
The worker and the barrel are in an initial state of rest, which means the initial kinetic energy is zero. The only energy at play at the start is gravitational potential energy. As the system is allowed to evolve, the gravitational potential energy of the worker will decrease as he falls, while the speed – and therefore the kinetic energy – of both objects will increase.
Considering energy conservation, the initial potential energy of the system will be equal to the combined final kinetic energy of both the worker and the barrel when the worker hits the ground:
- Initial PE = Final KE of worker + Final KE of barrel
The initial potential energy (PE_initial) can be determined for both the worker and the barrel as:
PE_initial = (mass of the worker * height * gravity) + (mass of the barrel * height * gravity)
The kinetic energy (KE) for both the worker and the barrel when the worker hits the ground will be:
KE = 0.5 * mass * velocity^2
Setting the initial potential energy equal to the sum of the final kinetic energies allows us to solve for the final velocity which will be the same for both the worker and the barrel due to the rope constraint.
To solve for the final velocity (v), we can use the formula:
PE_initial = KE_worker_final + KE_barrel_final
(m_worker * g * h) + (m_barrel * g * h) = 0.5 * m_worker * v^2 + 0.5 * m_barrel * v^2
After rearranging the terms and solving for v, we can find the final velocity at the moment the worker hits the ground. This can subsequently be inserted into a calculator to find a numerical value for the answer.