Final answer:
The kinetic energy of a 78 kg skydiver moving at 62 m/s is 150,132 J, and their potential energy at an altitude of 870 m is 668,481.6 J. The total mechanical energy is the sum of kinetic and potential energy, which in this case is 818,613.6 J.
Step-by-step explanation:
To calculate the skydiver’s kinetic and potential energy, we use the formulas for kinetic energy (KE) and gravitational potential energy (PE). The formula for kinetic energy is KE = ½mv², where m is the mass of the skydiver and v is the velocity. The formula for potential energy is PE = mgh, where g is the acceleration due to gravity (9.81 m/s²) and h is the altitude.
(a) To calculate the kinetic energy of a 78 kg skydiver moving at 62 m/s, we use the formula:
KE = ½ × 78 kg × (62 m/s)² = ½ × 78 kg × 3844 m²/s² = 150,132 J
(b) To calculate the potential energy at an altitude of 870 m:
PE = 78 kg × 9.81 m/s² × 870 m = 668,481.6 J
(c) The total mechanical energy (TME) is the sum of the kinetic and potential energy:
TME = KE + PE = 150,132 J + 668,481.6 J = 818,613.6 J
Therefore, the total mechanical energy of the skydiver is 818,613.6 J.