Question

a parachutist of mass 100 kg falls from a height of 500 m. under realistic conditions, she experiences air resistance. based on what you know about friction, what can you say about the kinetic energy of the parachutist as she reaches the ground? remember, 1 kj = 1000 j. acceleration due to gravity is ( g = 9.8 m/s^{2} ).

a. ( ke = 490 kj )
b. ( ke < 490 kj )
c. ( ke > 490 kj )
d. ( ke = 0 j )

Explanation:

Step1: Calculate potential energy

Potential energy formula \( PE = mgh \). Given \( m = 100\ \text{kg} \), \( g=9.8\ \text{m/s}^2 \), \( h = 500\ \text{m} \).
\( PE=100\times9.8\times500 = 490000\ \text{J}=490\ \text{kJ} \).

Step2: Consider energy loss

In reality, air - resistance (a non - conservative force) does work against the motion of the parachutist. According to the work - energy theorem \( \Delta E=\text{Work done by non - conservative forces} \). The total mechanical energy \( E = KE+PE \). At the height \( h = 500\ \text{m} \), \( E = PE\) (initial \( KE = 0\)). As she falls, some of the initial potential energy is converted into kinetic energy and some is dissipated as heat (due to air - resistance). So \( KE=PE-\text{Energy lost due to air - resistance}\).

Since energy lost due to air - resistance \(>0\), \( KE<490\ \text{kJ}\).

Answer:

B. \( KE < 490\ \text{kJ} \)