Question

Тіло масою 6кг починає вільно падати з висоти 30м. Якою буде його швидкість на висоті 15м? Прийняти g = 10H/кг

Answer 1

Ответ:

15м/с

Объяснение:

Answer 2

Calculation of Velocity using the Law of Conservation of Energy

To calculate the velocity of an object falling freely from a given height, we can use the law of conservation of energy. According to this law, the total mechanical energy of the object remains constant throughout its motion. The mechanical energy is the sum of the object's potential energy (PE) and kinetic energy (KE).

At the initial height of 30m, the object has only potential energy, which can be calculated using the formula:

PE = mgh

Where: - PE is the potential energy - m is the mass of the object (6kg) - g is the acceleration due to gravity (10m/s^2) - h is the height (30m)

Substituting the given values into the formula, we get:

PE = 6kg * 10m/s^2 * 30m = 1800 Joules

At a height of 15m, the object still has potential energy, but it has also gained kinetic energy. The potential energy at this height can be calculated using the same formula:

PE = mgh

Where: - PE is the potential energy - m is the mass of the object (6kg) - g is the acceleration due to gravity (10m/s^2) - h is the height (15m)

Substituting the given values into the formula, we get:

PE = 6kg * 10m/s^2 * 15m = 900 Joules

Since the total mechanical energy remains constant, we can equate the potential energy at the initial height to the sum of the potential energy and kinetic energy at the height of 15m:

1800 Joules = 900 Joules + KE

Simplifying the equation, we find:

KE = 900 Joules

The kinetic energy can be calculated using the formula:

KE = (1/2)mv^2

Where: - KE is the kinetic energy - m is the mass of the object (6kg) - v is the velocity

Substituting the given values into the formula, we get:

900 Joules = (1/2) * 6kg * v^2

Simplifying the equation, we find:

v^2 = 300 Joules / 6kg = 50 m^2/s^2

Taking the square root of both sides, we find:

v = sqrt(50 m^2/s^2) = 7.07 m/s

Therefore, the velocity of the object at a height of 15m will be approximately 7.07 m/s.

Conclusion

The velocity of the object at a height of 15m will be approximately 7.07 m/s.