Question

Мяч брошен вертикально вверх со скоростью 13м/с.Найти скорость мяча на высоте 300 см

Answer 1

Finding the velocity of a ball at a height of 300 cm

To find the velocity of a ball at a height of 300 cm, we can use the principles of projectile motion and conservation of energy.

Let's assume that the ball is thrown vertically upwards with an initial velocity of 13 m/s. At the highest point of its trajectory, the ball will momentarily come to rest before falling back down. At this point, all of its initial kinetic energy will be converted into potential energy.

Using the conservation of energy, we can equate the initial kinetic energy to the potential energy at the highest point:

Initial kinetic energy = Potential energy at the highest point

The initial kinetic energy can be calculated using the formula:

Kinetic energy = (1/2) * mass * velocity^2

Since the mass of the ball is not given, we can assume it to be 1 kg for simplicity.

Now, let's calculate the initial kinetic energy:

Initial kinetic energy = (1/2) * 1 kg * (13 m/s)^2

Simplifying the equation:

Initial kinetic energy = 0.5 * 1 kg * 169 m^2/s^2

Initial kinetic energy = 84.5 J

At the highest point, the ball's potential energy is given by:

Potential energy = mass * gravity * height

Since the height is given as 300 cm, we need to convert it to meters:

Height = 300 cm = 3 m

Now, let's calculate the potential energy at the highest point:

Potential energy = 1 kg * 9.8 m/s^2 * 3 m

Simplifying the equation:

Potential energy = 29.4 J

Since the initial kinetic energy is equal to the potential energy at the highest point, we can equate the two values:

Initial kinetic energy = Potential energy

84.5 J = 29.4 J

Simplifying the equation:

84.5 J = 29.4 J

84.5 J - 29.4 J = 0

This equation is not true, which means there is an error in the calculations or assumptions made. Let's try again using a different approach.

Alternative Approach

Another way to find the velocity of the ball at a height of 300 cm is to use the equations of motion. We can use the equation for vertical motion:

v^2 = u^2 + 2as

Where: - v is the final velocity (which we want to find) - u is the initial velocity (13 m/s) - a is the acceleration due to gravity (-9.8 m/s^2, taking into account the direction) - s is the displacement (300 cm = 3 m)

Rearranging the equation to solve for v:

v^2 = u^2 + 2as

v^2 = (13 m/s)^2 + 2 * (-9.8 m/s^2) * 3 m

v^2 = 169 m^2/s^2 - 58.8 m^2/s^2

v^2 = 110.2 m^2/s^2

Taking the square root of both sides to find v:

v = √(110.2 m^2/s^2)

v ≈ 10.5 m/s

Therefore, the velocity of the ball at a height of 300 cm is approximately 10.5 m/s.

Please note that the calculations made here are based on the given information and assumptions. If there are any additional factors or details that need to be considered, the answer may vary.