Question

Вася кинул камень под углом 45° к горизонту со скоростью 10 м/с. Определи какое расстояние пролетит камень. Сопротивлением воздуха принебречь. Камень упал и летел над абсолютно ровной поверхностью.

Answer 1

Т.к. ∠α=45°, то Vоx=Vоy=Vo*sinα=10 * √2/2=5√2 м/с.

Время подъема.

Vy=Voy - gt; в высшей точке Vy=0

0=5√2 - 10t

10t=5√2

t=√2/2

Время полёта: время подъема + такое же время падения

2t=√2 c.

Дальность

L=Vox * 2t=5√2 * √2=5*2=10 м  -  это ответ.

Или

готовая формула:

L=Vo²*sin2α/g=10²*sin90 / 10=10 м.

Но лучше самим подсчитать.

Answer 2

Calculation of the Distance Traveled by the Stone

To determine the distance traveled by the stone, we can use the equations of projectile motion. Given that the stone was thrown at an angle of 45° to the horizontal with an initial velocity of 10 m/s, we can calculate the horizontal and vertical components of its velocity.

The horizontal component of the velocity remains constant throughout the motion, while the vertical component changes due to the effect of gravity. At the highest point of the stone's trajectory, the vertical component of its velocity becomes zero.

Using the equations of motion, we can calculate the time taken for the stone to reach its highest point and the total time of flight. With these values, we can then calculate the horizontal distance traveled by the stone.

Let's break down the calculation step by step:

1. Calculate the initial vertical velocity (Vy) and initial horizontal velocity (Vx) using the given angle and initial velocity: - Vy = V * sin(θ) - Vx = V * cos(θ)

In this case, θ = 45° and V = 10 m/s, so: - Vy = 10 * sin(45°) - Vx = 10 * cos(45°)

2. Calculate the time taken to reach the highest point (t_max) using the equation: - t_max = Vy / g

Here, g represents the acceleration due to gravity, which is approximately 9.8 m/s².

3. Calculate the total time of flight (t_total) using the equation: - t_total = 2 * t_max

Since the stone reaches its highest point and returns to the same height, the total time of flight is twice the time taken to reach the highest point.

4. Calculate the horizontal distance traveled (d) using the equation: - d = Vx * t_total

Now, let's calculate the values:

1. Calculate Vy and Vx: - Vy = 10 * sin(45°) - Vx = 10 * cos(45°)

Using a calculator, we find that Vy and Vx are both approximately 7.07 m/s.

2. Calculate t_max: - t_max = 7.07 / 9.8

Using a calculator, we find that t_max is approximately 0.72 seconds.

3. Calculate t_total: - t_total = 2 * 0.72

Using a calculator, we find that t_total is approximately 1.44 seconds.

4. Calculate d: - d = 7.07 * 1.44

Using a calculator, we find that the horizontal distance traveled by the stone is approximately 10.17 meters.

Therefore, the stone will travel approximately 10.17 meters horizontally before hitting the ground, assuming no air resistance and a perfectly flat surface.

Please note that the above calculations are based on the assumption of ideal projectile motion and neglect the effects of air resistance and other factors that may affect the actual distance traveled by the stone.