A 65 kg diver stand still on a tower 10.0 m above the water. A. Calculate the gravitational potential energy of the diver relative to the height of the water assume the gravitational field constant is 9.8.N/kg . B. The diver reaches the surface of the water at a speed of 14m/s . Calculate the divers kinetic energy. C. Compare your answers to an and B. Explain your comparison using concepts learned in this course. Assume there is no air resistance during Compare your answers to an and B. Explain your comparison using concepts learned in this course. Assume there is no air resistance during the dive. D. Calculate the speed of the diver 5.0 m above the water.
A. The gravitational potential energy is given by the equation:
Gravitational potential energy = mass * gravitational field constant * height
Plugging in the values, we have:
Gravitational potential energy = 65 kg * 9.8 N/kg * 10.0 m = 6370 J
B. The kinetic energy is given by the equation:
Kinetic energy = (1/2) * mass * velocity^2
Plugging in the values, we have:
Kinetic energy = (1/2) * 65 kg * (14 m/s)^2 = 6370 J
C. The gravitational potential energy and the kinetic energy of the diver are the same, which can be explained using the principle of conservation of energy. The total mechanical energy of the diver remains constant throughout the dive since there is no external work done on the system. As the diver falls, gravitational potential energy is converted into kinetic energy.
D. To calculate the speed of the diver 5.0 m above the water, we can use the principle of conservation of mechanical energy. At that point, the gravitational potential energy is equal to the kinetic energy.
Gravitational potential energy = Kinetic energy
mass * gravitational field constant * height = (1/2) * mass * velocity^2
Substituting the known values, we have:
65 kg * 9.8 N/kg * 5.0 m = (1/2) * 65 kg * velocity^2
Simplifying, we find:
3135 N = 32.5 kg * velocity^2
Dividing both sides by 32.5 kg and taking the square root, we find:
velocity = √(3135 N / 32.5 kg) = 8.42 m/s