Question

После удара клюшкой шайба стала скользить вверх по ледяной горке и у ее вершины имела скорость 10 м/с. Какова высота горки, если после удара скорость шайбы равнялась 20 м/с. Трение шайбы о лёд пренебрежимо мало.

Answer 1

А угла наклона горки нет ? 

Answer 2

Calculation of the Height of the Slope

To calculate the height of the slope, we can use the principle of conservation of mechanical energy. The initial mechanical energy of the puck is equal to its final mechanical energy.

The initial mechanical energy of the puck is given by the sum of its kinetic energy and potential energy at the top of the slope. The final mechanical energy of the puck is given by its kinetic energy at the bottom of the slope.

Let's denote the height of the slope as h.

At the top of the slope: - The potential energy is zero since the puck is at the top. - The kinetic energy is given by 1/2 * m * v^2, where m is the mass of the puck and v is the velocity of the puck at the top.

At the bottom of the slope: - The potential energy is given by m * g * h, where g is the acceleration due to gravity. - The kinetic energy is given by 1/2 * m * v^2, where v is the velocity of the puck at the bottom.

According to the principle of conservation of mechanical energy, the initial mechanical energy is equal to the final mechanical energy:

1/2 * m * v1^2 + 0 = 0 + m * g * h + 1/2 * m * v2^2

Given that the initial velocity (v1) is 10 m/s and the final velocity (v2) is 20 m/s, we can rewrite the equation as:

1/2 * m * (20)^2 = m * g * h + 1/2 * m * (10)^2

Simplifying the equation:

200 = g * h + 50

Rearranging the equation to solve for h:

h = (200 - 50) / g

Since the question states that the friction between the puck and the ice is negligible, we can assume that the only force acting on the puck is the force due to gravity. Therefore, the acceleration due to gravity g is approximately 9.8 m/s^2.

Substituting the value of g into the equation:

h = (200 - 50) / 9.8

Calculating the value of h:

h ≈ 15.31 meters

Therefore, the height of the slope is approximately 15.31 meters.