Question

Кинетическая энергия лыжника массой 80 кг после спуска с горы составляет 4 кдж ,определить его скорость движения и высоты горы .трением пренебречь

Answer 1

Кинетическая энергия=m(масса)*u(скорость)в квадрате/2
отсюда скорость в квадрате =(4000*2):80=100м/с значит скорость лыжника равна 10м/с
кинетеческая энергия=работе значит A=F*S=4000отсюда S=4000/(80*10)=5Метров
ответ 10м/с и 5 метров

Answer 2

Calculation of the Skier's Speed and Mountain Height

To determine the skier's speed and the height of the mountain, we can use the principle of conservation of energy. According to this principle, the total energy of a system remains constant, assuming no external forces are acting on it. In this case, we can assume that there is no friction, so we can neglect its effects.

The total energy of the skier can be divided into two parts: potential energy (PE) and kinetic energy (KE). The potential energy is given by the formula PE = mgh, where m is the mass of the skier, g is the acceleration due to gravity, and h is the height of the mountain. The kinetic energy is given by the formula KE = (1/2)mv^2, where v is the speed of the skier.

Since the skier starts at the top of the mountain with no initial speed, all the initial energy is in the form of potential energy. After descending the mountain, the skier's potential energy is converted into kinetic energy.

We are given that the skier's kinetic energy after the descent is 4 kJ and the skier's mass is 80 kg. We need to find the skier's speed (v) and the height of the mountain (h).

Using the formula for kinetic energy, we can write:

KE = (1/2)mv^2

Substituting the given values:

4 kJ = (1/2) * 80 kg * v^2

Simplifying the equation:

v^2 = (4 kJ * 2) / (80 kg) v^2 = 0.1 kJ/kg

Taking the square root of both sides:

v = √(0.1 kJ/kg)

Now, let's calculate the skier's speed:

v = √(0.1 kJ/kg) ≈ 0.316 km/s

To find the height of the mountain, we can use the formula for potential energy:

PE = mgh

Substituting the given values:

4 kJ = 80 kg * 9.8 m/s^2 * h

Simplifying the equation:

h = (4 kJ) / (80 kg * 9.8 m/s^2) h = 0.0051 km

Converting the height to meters:

h = 0.0051 km * 1000 m/km h ≈ 5.1 m

Therefore, the skier's speed is approximately 0.316 km/s and the height of the mountain is approximately 5.1 meters.

Please note that these calculations assume no external forces such as air resistance or friction.