Let's break down the problem step by step, based on the provided information and results.
1. Total Energy Calculation:
- The woman initially has a kinetic energy (KE) of 2500 joules.
- Potential energy (PE) at this point is given as 0 joules (assuming she is at the lowest possible point where all energy is kinetic).
- Therefore, the total mechanical energy (E) is KE_initial + PE_initial, which is [tex]\(2500 \text{ joules} + 0 \text{ joules} = 2500 \text{ joules}\)[/tex].
2. Kinetic Energy Change:
- The question states the woman's kinetic energy reduces to 1000 joules.
- Since total energy is conserved, the remaining energy must be converted into potential energy.
3. Potential Energy Calculation:
- Originally, the total mechanical energy is 2500 joules.
- When the kinetic energy is 1000 joules, the potential energy (PE_final) can be found using the conservation of energy. The total energy remains constant and is [tex]\(2500 \text{ joules}\)[/tex].
- So, [tex]\( \text{PE_final} = \text{Total Energy} - \text{KE_final} \)[/tex].
- Plugging in the values, [tex]\( \text{PE_final} = 2500 \text{ joules} - 1000 \text{ joules} = 1500 \text{ joules} \)[/tex].
Therefore, when the woman's kinetic energy is 1000 joules, her potential energy is 1500 joules.
4. Effect of a Parachute:
- A parachute increases air resistance or drag. This reduces the speed at which the woman falls.
- As kinetic energy is proportional to the square of speed ([tex]\(KE = \frac{1}{2} mv^2\)[/tex]), reducing the speed reduces the kinetic energy.
- When using a parachute, the woman's descent is slower, and thus, her kinetic energy will be lower compared to a situation without a parachute.
- This change would result in a higher potential energy at the same point in the descent, reflecting the slower speed and reduced kinetic energy.
In summary:
- Total mechanical energy is 2500 joules.
- Initial kinetic energy is 2500 joules with zero potential energy.
- When kinetic energy reduces to 1000 joules, potential energy becomes 1500 joules.
- A parachute reduces the woman's kinetic energy by increasing air resistance, thus causing a slower descent.
