Final answer:
The kinetic energy of the skier just before reaching the ground, calculated using the conservation of energy principle and an approximation for gravity, is closest to option B) 13,860 J; however, the exact value would differ if we used 9.8 m/s² for gravity instead of 10 m/s².
Step-by-step explanation:
The skier's kinetic energy just before reaching the ground can be found using the principle of conservation of energy. The potential gravitational energy at the starting height is converted into kinetic energy as the skier descends. We calculate the initial potential energy using the equation PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s² by convention, but rounded to 10 m/s² for simplicity in this problem), and h is the height. Therefore, the kinetic energy (KE) just before reaching the ground is equal to the potential energy at the starting height.
Using the given values, the kinetic energy is calculated as KE = mgh = (69 kg) × (10 m/s²) × (20 m) = 13,800 J.
The answer closest to this calculation is B) 13,860 J. However, we should note that by using the standard acceleration due to gravity (9.8 m/s²), the precise answer would be different, and none of the options given exactly match the calculation using the exact value of g. Options A, C, and D can be ruled out based on the approximation used in this scenario.