Question

Мальчик на коньках разгоняется до скорости 11 м/с и вкатывается на ледяную горку. До какой высоты он сможет подняться, если коэффициент трения равен 0,1, а угол наклона горки к горизонту 45°?

Answer 1

м\с α=45µ=0,1 решение  s=172.8(м)

Answer 2

Calculation of the Maximum Height

To calculate the maximum height the boy can reach on the icy slope, we can use the principles of conservation of mechanical energy. The initial kinetic energy of the boy on skates will be converted into potential energy as he moves up the slope.

The formula for potential energy is given by:

Potential Energy (PE) = Mass (m) * Gravity (g) * Height (h)

The formula for kinetic energy is given by:

Kinetic Energy (KE) = 0.5 * Mass (m) * Velocity (v)^2

Since the boy is on skates, we can assume his mass is negligible compared to the other factors. Therefore, we can ignore the mass in our calculations.

At the bottom of the slope, the boy's kinetic energy is given by:

KE = 0.5 * Velocity^2

At the maximum height, the boy's kinetic energy is zero, and all the initial kinetic energy is converted into potential energy:

PE = Mass * Gravity * Height

Since we can ignore the mass, we can rewrite the equation as:

PE = Gravity * Height

Setting the initial kinetic energy equal to the potential energy at the maximum height, we have:

0.5 * Velocity^2 = Gravity * Height

Solving for the height, we get:

Height = (0.5 * Velocity^2) / Gravity

Now we can substitute the given values into the equation to find the maximum height.

Given: - Velocity (v) = 11 m/s - Coefficient of friction (μ) = 0.1 - Angle of inclination (θ) = 45°

First, we need to calculate the effective angle of inclination, taking into account the coefficient of friction. The effective angle of inclination (θ') can be calculated using the formula:

θ' = arctan(μ)

Substituting the given value of the coefficient of friction, we have:

θ' = arctan(0.1)

Using a calculator, we find:

θ' ≈ 5.71°

Now we can calculate the maximum height using the formula:

Height = (0.5 * Velocity^2) / Gravity

Substituting the given values, we have:

Height = (0.5 * 11^2) / 9.8

Calculating this expression, we find:

Height ≈ 6.02 meters

Therefore, the boy will be able to reach a maximum height of approximately 6.02 meters on the icy slope.