A parachutist of mass 50.0 kg jumps out of an airplane at a height of 1000 m . The parachute deploys, and she lands on the ground with a speed of \( 5.0 \mathrm{~m} / \mathrm{s} \). How much energy was lost to air friction during this jump? 1) 49400 J 2) 98700 J 3) 198000 J 4) 489000 J 5) 534000 J

To find out how much energy was lost to air friction during the parachutist's jump, we need to calculate the gravitational potential energy at the beginning of the jump and the kinetic energy just before landing. 1. **Gravitational Potential Energy (GPE)** at the height of 1000 m: \[ \text{GPE} = mgh = 50.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 1000 \, \text{m} = 490500 \, \text{J} \] 2. **Kinetic Energy (KE)** when landing at 5 m/s: \[ \text{KE} = \frac{1}{2} mv^2 = \frac{1}{2} \times 50.0 \, \text{kg} \times (5.0 \, \text{m/s})^2 = 1250 \, \text{J} \] 3. **Energy lost to air friction** can be calculated by subtracting the kinetic energy from the gravitational potential energy: \[ \text{Energy lost} = \text{GPE} - \text{KE} = 490500 \, \text{J} - 1250 \, \text{J} = 489250 \, \text{J} \] This rounds to approximately 489000 J. Therefore, the energy lost to air friction is closest to option 4) 489000 J. **So the answer is:** 4) 489000 J.