Question

Лыжник съезжает с горы высотой 10 м без начальной скорости. Какую скорость он приобретет у подножья горы?

Answer 1

Думаю 10 метров в секунду

Answer 2

Calculation of the Skier's Final Velocity

To calculate the skier's final velocity at the base of the mountain, we can use the principles of conservation of energy. At the top of the mountain, the skier has gravitational potential energy due to their height. As the skier descends, this potential energy is converted into kinetic energy, which is given by the equation:

Potential Energy = Kinetic Energy

The potential energy is given by the formula:

Potential Energy = mgh

Where: - m is the mass of the skier, - g is the acceleration due to gravity (approximately 9.8 m/s^2), - h is the height of the mountain (10 m in this case).

The kinetic energy is given by the formula:

Kinetic Energy = (1/2)mv^2

Where: - m is the mass of the skier, - v is the final velocity of the skier at the base of the mountain.

Since the skier starts from rest, the initial velocity is zero. Therefore, the initial kinetic energy is zero.

Setting the potential energy equal to the kinetic energy, we can solve for the final velocity:

mgh = (1/2)mv^2

Cancelling out the mass, we get:

gh = (1/2)v^2

Simplifying further:

v^2 = 2gh

Taking the square root of both sides:

v = sqrt(2gh)

Now we can substitute the given values into the equation to find the final velocity.

Calculation:

Given: - Height of the mountain (h) = 10 m - Acceleration due to gravity (g) = 9.8 m/s^2

Substituting these values into the equation:

v = sqrt(2 * 9.8 * 10)

Calculating the result:

v ≈ 14 m/s

Therefore, the skier will acquire a final velocity of approximately 14 m/s at the base of the mountain.

Please note that this calculation assumes no air resistance or other external factors affecting the skier's motion.