Question
65 kg diversity and still on a tower, 10.0 m above the water.
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Answer
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 answers to ANB. Explain your comparison using concepts learned in this course assume that there is no air resistance during the dive. D. Calculate the speed of the diver 5.0 m above the water.
Answered by
GPT 3.5
I'm sorry, but I'm not sure what you mean by "65 kg diversity" in this context. Could you please provide more information or clarify your question?
Answered by
GPT 3.5
A. To calculate the gravitational potential energy of the diver relative to the height of the water, we can use the formula:
Gravitational Potential Energy = mass * gravitational field constant * height
Given that the mass of the diver is 65 kg, the gravitational field constant is 9.8 N/kg, and the height is 10.0 m, we can calculate the gravitational potential energy:
Gravitational Potential Energy = 65 kg * 9.8 N/kg * 10.0 m
Gravitational Potential Energy = 6370 J
Therefore, the gravitational potential energy of the diver relative to the height of the water is 6370 J.
B. To calculate the diver's kinetic energy, we can use the formula:
Kinetic Energy = 0.5 * mass * velocity^2
Given that the mass of the diver is 65 kg and the speed at which the diver reaches the surface of the water is 14 m/s, we can calculate the kinetic energy:
Kinetic Energy = 0.5 * 65 kg * (14 m/s)^2
Kinetic Energy = 6370 J
Therefore, the diver's kinetic energy is 6370 J.
C. Comparing the answers to A and B, we can see that the gravitational potential energy and the kinetic energy are equal. This relationship can be explained by the conservation of energy principle, which states that energy cannot be created or destroyed, but only converted from one form to another. In this case, as the diver falls from the tower to the water, potential energy is converted into kinetic energy, resulting in the two energies being equal.
D. To calculate the speed of the diver 5.0 m above the water, we can use the conservation of energy. At that point, the gravitational potential energy will be equal to the kinetic energy:
Gravitational Potential Energy = Kinetic Energy
m * g * h = 0.5 * m * v^2
Given that the height is 5.0 m and the gravitational field constant is 9.8 N/kg, we can solve for the velocity (v):
65 kg * 9.8 N/kg * 5.0 m = 0.5 * 65 kg * v^2
v^2 = (65 kg * 9.8 N/kg * 5.0 m) / (0.5 * 65 kg)
v^2 = (3205 N * m) / (32.5 kg)
v^2 = 98.46 m^2/s^2
Taking the square root of both sides, we find:
v = √(98.46 m^2/s^2)
v ≈ 9.92 m/s
Therefore, the speed of the diver 5.0 m above the water is approximately 9.92 m/s.
Gravitational Potential Energy = mass * gravitational field constant * height
Given that the mass of the diver is 65 kg, the gravitational field constant is 9.8 N/kg, and the height is 10.0 m, we can calculate the gravitational potential energy:
Gravitational Potential Energy = 65 kg * 9.8 N/kg * 10.0 m
Gravitational Potential Energy = 6370 J
Therefore, the gravitational potential energy of the diver relative to the height of the water is 6370 J.
B. To calculate the diver's kinetic energy, we can use the formula:
Kinetic Energy = 0.5 * mass * velocity^2
Given that the mass of the diver is 65 kg and the speed at which the diver reaches the surface of the water is 14 m/s, we can calculate the kinetic energy:
Kinetic Energy = 0.5 * 65 kg * (14 m/s)^2
Kinetic Energy = 6370 J
Therefore, the diver's kinetic energy is 6370 J.
C. Comparing the answers to A and B, we can see that the gravitational potential energy and the kinetic energy are equal. This relationship can be explained by the conservation of energy principle, which states that energy cannot be created or destroyed, but only converted from one form to another. In this case, as the diver falls from the tower to the water, potential energy is converted into kinetic energy, resulting in the two energies being equal.
D. To calculate the speed of the diver 5.0 m above the water, we can use the conservation of energy. At that point, the gravitational potential energy will be equal to the kinetic energy:
Gravitational Potential Energy = Kinetic Energy
m * g * h = 0.5 * m * v^2
Given that the height is 5.0 m and the gravitational field constant is 9.8 N/kg, we can solve for the velocity (v):
65 kg * 9.8 N/kg * 5.0 m = 0.5 * 65 kg * v^2
v^2 = (65 kg * 9.8 N/kg * 5.0 m) / (0.5 * 65 kg)
v^2 = (3205 N * m) / (32.5 kg)
v^2 = 98.46 m^2/s^2
Taking the square root of both sides, we find:
v = √(98.46 m^2/s^2)
v ≈ 9.92 m/s
Therefore, the speed of the diver 5.0 m above the water is approximately 9.92 m/s.
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