Question

Камень брошенный с вышки горизонтально со скоростью 10м/с , упал на землю под углом 45градусов. Определите скорость падения камня...

Answer 1

Горизонтально составляющая скорость не меняется, следовательно, т.к. угол= 45 гр, то м=10/cos45=14,1 м/c

Answer 2

Problem Analysis

We are given that a stone is thrown horizontally from a tower with a velocity of 10 m/s and it falls to the ground at an angle of 45 degrees. We need to determine the speed at which the stone hits the ground.

Solution

To solve this problem, we can break down the motion of the stone into its horizontal and vertical components. Since the stone is thrown horizontally, its initial vertical velocity is zero. The only force acting on the stone is gravity, which causes it to accelerate vertically downwards.

Let's analyze the horizontal and vertical components separately.

# Horizontal Component

Since the stone is thrown horizontally, its initial horizontal velocity is 10 m/s and remains constant throughout its motion. Therefore, the horizontal component of the stone's velocity is 10 m/s.

# Vertical Component

The stone falls to the ground under the influence of gravity. The vertical motion of the stone can be analyzed using the equations of motion for uniformly accelerated motion.

We can use the following equation to find the time of flight (t) of the stone: t = 2 * (v_y) / g where v_y is the vertical component of the stone's velocity and g is the acceleration due to gravity (approximately 9.8 m/s^2).

To find the vertical component of the stone's velocity (v_y), we can use the following equation: v_y = v * sin(θ) where v is the initial velocity of the stone (10 m/s) and θ is the angle at which the stone hits the ground (45 degrees).

Using these equations, we can calculate the time of flight and the vertical component of the stone's velocity.

# Calculation

Let's calculate the time of flight (t) and the vertical component of the stone's velocity (v_y):

Given: - Initial velocity (v) = 10 m/s - Angle (θ) = 45 degrees - Acceleration due to gravity (g) = 9.8 m/s^2

Using the equation v_y = v * sin(θ), we can calculate v_y: v_y = 10 m/s * sin(45 degrees) = 10 m/s * 0.7071 ≈ 7.071 m/s

Using the equation t = 2 * (v_y) / g, we can calculate t: t = 2 * (7.071 m/s) / 9.8 m/s^2 ≈ 1.44 s

Therefore, the time of flight of the stone is approximately 1.44 seconds, and the vertical component of the stone's velocity is approximately 7.071 m/s.

# Final Answer

The speed at which the stone hits the ground is equal to the vertical component of its velocity, which is approximately 7.071 m/s.

Note: The above calculations assume ideal conditions and neglect air resistance.