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To determine the gravitational potential energy (PE) of a 65 kg diver standing on a tower 10.0 m above the water, we use the formula PE = m * g * h, where m is the mass, g is the gravitational field constant (9.8 N/kg), and h is the height. Substituting the values, we calculate PE = 65 kg * 9.8 N/kg * 10.0 m = 6370 J. For the kinetic energy (KE) of the diver upon reaching the water at a speed of 14 m/s, we use the formula KE = 0.5 * m * v^2. This gives us KE = 0.5 * 65 kg * (14 m/s)^2 = 6370 J. Comparing the two energies, both the potential and kinetic energies equal 6370 J, illustrating the principle of conservation of mechanical energy. This principle states that in the absence of non-conservative forces, the total mechanical energy of the diver remains constant, with potential energy converting into kinetic energy during the dive. To find the speed of the diver 5.0 m above the water, we again apply energy conservation. At this height, the potential energy is PE' = 65 kg * 9.8 N/kg * 5.0 m = 3190 J. The total energy when diving starts at the top is E_total = 6370 J. Thus, the kinetic energy at 5.0 m is KE' = E_total - PE' = 6370 J - 3190 J = 3180 J. Using KE' = 0.5 * m * v'^2, we solve for v', giving us 3180 J = 0.5 * 65 kg * v'^2. This results in v'^2 = (2 * 3180) / 65 ≈ 97.54, leading to v' ≈ √97.54 ≈ 9.87 m/s. Therefore, the speed of the diver 5.0 m above the water is approximately 9.87 m/s.

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To find out how much gravitational potential energy (PE) a 65 kg diver has when standing on a tower 10.0 m above the water, we use the formula PE = m * g * h. Here, "m" is the mass of the diver, "g" is the gravitational force (which is about 9.8 N/kg), and "h" is the height above the water. By putting in the numbers, we find that PE = 65 kg * 9.8 N/kg * 10.0 m, which equals 6370 joules (J). 

Now, when the diver jumps and reaches the water at a speed of 14 m/s, we calculate the kinetic energy (KE) using the formula KE = 0.5 * m * v^2. Plugging in the values gives us KE = 0.5 * 65 kg * (14 m/s)^2, which also equals 6370 J. This shows that both the potential and kinetic energies are the same at 6370 J because of the principle of conservation of mechanical energy. This principle means that if there are no outside forces acting on the diver, the total mechanical energy stays the same. The potential energy changes into kinetic energy when the diver jumps.

Next, to find the speed of the diver when he is 5.0 m above the water, we again use energy conservation. At this height, we find the potential energy to be PE' = 65 kg * 9.8 N/kg * 5.0 m, which equals 3190 J. The total energy when the dive starts is still 6370 J. So, the kinetic energy at 5.0 m is KE' = total energy - PE' = 6370 J - 3190 J, which equals 3180 J. Now, to find the speed (v') at this height, we use the formula KE' = 0.5 * m * v'^2. Plugging in the numbers, we get 3180 J = 0.5 * 65 kg * v'^2. Simplifying this, we find v'^2 = (2 * 3180) / 65 which is about 97.54. Finally, taking the square root gives us v' ≈ 9.87 m/s. So, the diver's speed when he is 5.0 m above the water is about 9.87 m/s.
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Sure! Here it is broken down into even simpler steps and words:

To find out how much potential energy (PE) a 65 kg diver has when he is on a tower 10.0 m high, we use this formula: PE = m * g * h. In this formula, "m" is the mass of the diver (65 kg), "g" is the force of gravity (about 9.8 N/kg), and "h" is the height (10 m). So, we calculate: 
PE = 65 kg * 9.8 N/kg * 10 m = 6370 joules (J). 

Now, when the diver jumps and hits the water going 14 m/s, we find his kinetic energy (KE) using this formula: KE = 0.5 * m * v^2. Plugging in the numbers gives us: 
KE = 0.5 * 65 kg * (14 m/s)^2 = 6370 J. 

This tells us that both the potential energy and kinetic energy are 6370 J. This shows that energy stays the same when there are no outside forces acting on the diver. The energy change from potential to kinetic happens as he jumps.

Next, we want to know the diver's speed when he is 5.0 m above the water. First, we find his potential energy at that height: 
PE' = 65 kg * 9.8 N/kg * 5.0 m = 3190 J. 

Since the total energy at the start is still 6370 J, we can find the kinetic energy (KE') at 5.0 m:
KE' = total energy - PE' = 6370 J - 3190 J = 3180 J. 

Now we find the speed (v') using KE' = 0.5 * m * v'^2. So we have:
3180 J = 0.5 * 65 kg * v'^2. 

Solving this, we get:
v'^2 = (2 * 3180) / 65 ≈ 97.54. 

Taking the square root gives us v' ≈ 9.87 m/s. So, the diver's speed when he is 5.0 m above the water is about 9.87 m/s.