Question

Спортсмен массой 60 кг прыгает с 10-метровой вышки в воду. Чему равны: потенциальная энергия спортсмена относительно поверхности воды перед прыжком; его кинетическая энергия при вхождении в воду; его потенциальная и кинетическая энергия на высоте 5 м относительно поверхности воды? Сопротивлением воздуха пренебречь.

Answer 1

на вершине вышки потенциалная энергия равна mgh=60*10*10=6000Дж

По закону сохранения энергии в самом конце полёта спортсмена Епот=0=>Екин=нач. потенициальная энергия.=6000Дж

На восоте 5 м Энергии кинетическая и потенциальная будут равны, т.к. потенциальная энергия будет равна mgh=60*5*10=3000Дж, а по закону сохранения энергии кин=6000Дж-3000Дж=3000Дж

 

Answer 2

Calculation of Potential Energy:

To calculate the potential energy of the athlete before the jump, we can use the formula:

Potential Energy = mass * gravity * height

Given: - Mass of the athlete (m) = 60 kg - Height of the diving board (h) = 10 m - Acceleration due to gravity (g) = 9.8 m/s^2

Using the formula, we can calculate the potential energy:

Potential Energy = 60 kg * 9.8 m/s^2 * 10 m

Calculating the above expression, we find that the potential energy of the athlete before the jump is 5880 Joules.

Calculation of Kinetic Energy upon Entry:

To calculate the kinetic energy of the athlete upon entry into the water, we can use the formula:

Kinetic Energy = 0.5 * mass * velocity^2

Given: - Mass of the athlete (m) = 60 kg - Velocity of the athlete upon entry (v) = ?

To calculate the velocity, we can use the principle of conservation of energy. At the top of the dive, all the potential energy is converted into kinetic energy. Therefore, the potential energy at the top is equal to the kinetic energy upon entry.

Using the formula for potential energy, we can equate it to the kinetic energy formula:

Potential Energy = Kinetic Energy m * g * h = 0.5 * m * v^2

Simplifying the equation, we find:

v = sqrt(2 * g * h)

Substituting the given values, we can calculate the velocity:

v = sqrt(2 * 9.8 m/s^2 * 10 m)

Calculating the above expression, we find that the velocity of the athlete upon entry is approximately 14 m/s.

Now, we can calculate the kinetic energy using the formula:

Kinetic Energy = 0.5 * 60 kg * (14 m/s)^2

Calculating the above expression, we find that the kinetic energy of the athlete upon entry into the water is 5880 Joules.

Calculation of Potential and Kinetic Energy at a Height of 5 m:

To calculate the potential and kinetic energy of the athlete at a height of 5 m above the water surface, we can use the same formulas as before.

Potential Energy: Potential Energy = mass * gravity * height

Given: - Mass of the athlete (m) = 60 kg - Height above the water surface (h) = 5 m - Acceleration due to gravity (g) = 9.8 m/s^2

Using the formula, we can calculate the potential energy:

Potential Energy = 60 kg * 9.8 m/s^2 * 5 m

Calculating the above expression, we find that the potential energy of the athlete at a height of 5 m is 2940 Joules.

Kinetic Energy: To calculate the kinetic energy at a height of 5 m, we need to know the velocity of the athlete at that height. Unfortunately, this information is not provided in the question. Therefore, we cannot calculate the kinetic energy at a height of 5 m without additional information.

Please provide the velocity of the athlete at a height of 5 m above the water surface in order to calculate the kinetic energy at that point.

Summary:

- The potential energy of the athlete before the jump is 5880 Joules. - The kinetic energy of the athlete upon entry into the water is 5880 Joules. - The potential energy of the athlete at a height of 5 m above the water surface is 2940 Joules. - The kinetic energy at a height of 5 m cannot be calculated without the velocity of the athlete at that point.