Question

Человек, сидящий в лодке, бросает камень под углом 45 гр. к горизонту с начальной скоростью 10 м/с. Масса камня 1 кг, масса человека и лодки 100 кг. Найти расстояние между местом падения камня и лодкой в момент времени, когда камень коснулся воды. Трением лодки о воду пренебречь. (10,1 м)

Answer 1

Problem Statement

We are given the following information: - A person sitting in a boat throws a stone at an angle of 45 degrees to the horizon. - The stone has an initial velocity of 10 m/s. - The mass of the stone is 1 kg, and the combined mass of the person and the boat is 100 kg. - We need to find the distance between the point where the stone hits the water and the boat at the moment the stone touches the water. - We can neglect the friction between the boat and the water.

Solution

To solve this problem, we can break it down into two components: the horizontal and vertical motion of the stone.

# Vertical Motion

In the vertical direction, we can use the equations of motion to find the time it takes for the stone to hit the water. Since the stone is thrown at an angle of 45 degrees, the initial vertical velocity is given by:

Initial vertical velocity (Vy) = initial velocity (V) * sin(angle)

Substituting the given values, we have:

Vy = 10 m/s * sin(45 degrees) = 10 m/s * 0.7071 ≈ 7.071 m/s

The time taken for the stone to reach the highest point can be found using the equation:

Time to reach highest point (t) = Vy / g

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the values, we have:

t = 7.071 m/s / 9.8 m/s^2 ≈ 0.721 seconds

Since the stone takes the same amount of time to reach the highest point and fall back to the water, the total time of flight is twice the time to reach the highest point:

Total time of flight (T) = 2 * t ≈ 2 * 0.721 seconds ≈ 1.442 seconds

# Horizontal Motion

In the horizontal direction, the initial horizontal velocity (Vx) is given by:

Initial horizontal velocity (Vx) = initial velocity (V) * cos(angle)

Substituting the given values, we have:

Vx = 10 m/s * cos(45 degrees) = 10 m/s * 0.7071 ≈ 7.071 m/s

The horizontal distance covered by the stone can be found using the equation:

Horizontal distance (D) = Vx * T

Substituting the values, we have:

D = 7.071 m/s * 1.442 seconds ≈ 10.2 meters

Therefore, the distance between the point where the stone hits the water and the boat at the moment the stone touches the water is approximately 10.2 meters.

Please note that the above calculations assume ideal conditions and neglect factors such as air resistance and the rotation of the Earth.