Question

С вершины горы под углом 30 к горизонту бросают мяч со скоростью 5 м\с. Высота горы 100м. На каком расстоянии от точки бросания упадёт мяч?

Answer 1

В этом случае можно рассчитать по формуле:S(дальность полета)=v0$\sqrt{2H/g}=5 * \sqrt{2*100/10}=10 \sqrt{5}$

Answer 2

Problem Analysis

We are given the following information: - The ball is thrown from the top of a mountain at an angle of 30 degrees to the horizon. - The initial velocity of the ball is 5 m/s. - The height of the mountain is 100 m.

We need to determine the distance from the point of throwing where the ball will fall.

Solution

To solve this problem, we can break down the initial velocity of the ball into its horizontal and vertical components. We can then use the equations of motion to calculate the time it takes for the ball to reach the ground.

Let's start by finding the horizontal and vertical components of the initial velocity.

The horizontal component of the velocity can be calculated using the formula:

Vx = V * cos(theta)

where: - Vx is the horizontal component of the velocity, - V is the initial velocity of the ball, and - theta is the angle of projection.

Substituting the given values, we have:

Vx = 5 m/s * cos(30 degrees)

To find the vertical component of the velocity, we can use the formula:

Vy = V * sin(theta)

where: - Vy is the vertical component of the velocity.

Substituting the given values, we have:

Vy = 5 m/s * sin(30 degrees)

Now, let's calculate the time it takes for the ball to reach the ground using the equation of motion:

h = Vy * t + (1/2) * g * t^2

where: - h is the height of the mountain, - Vy is the vertical component of the velocity, - t is the time taken for the ball to reach the ground, and - g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the given values, we have:

100 m = (5 m/s * sin(30 degrees)) * t + (1/2) * 9.8 m/s^2 * t^2

Simplifying the equation, we get a quadratic equation:

(1/2) * 9.8 m/s^2 * t^2 + (5 m/s * sin(30 degrees)) * t - 100 m = 0

We can solve this quadratic equation to find the time taken for the ball to reach the ground. Once we have the time, we can calculate the horizontal distance traveled by the ball using the formula:

distance = Vx * t

Let's calculate the values step by step.

Calculation

1. Calculate the horizontal component of the velocity:

Vx = 5 m/s * cos(30 degrees) = 5 m/s * 0.866 = 4.33 m/s

2. Calculate the vertical component of the velocity:

Vy = 5 m/s * sin(30 degrees) = 5 m/s * 0.5 = 2.5 m/s

3. Solve the quadratic equation to find the time taken for the ball to reach the ground:

(1/2) * 9.8 m/s^2 * t^2 + (2.5 m/s) * t - 100 m = 0

Using the quadratic formula, we find:

t = (-b ± sqrt(b^2 - 4ac)) / (2a)

where: - a = (1/2) * 9.8 m/s^2 = 4.9 m/s^2 - b = 2.5 m/s - c = -100 m

Substituting the values, we have:

t = (-2.5 ± sqrt((2.5)^2 - 4 * 4.9 * (-100))) / (2 * 4.9)

Simplifying the equation, we get:

t ≈ 5.1 s (ignoring the negative value)

4. Calculate the horizontal distance traveled by the ball:

distance = Vx * t = 4.33 m/s * 5.1 s ≈ 22.083 m

Therefore, the ball will fall at a distance of approximately 22.083 meters from the point of throwing.

Answer

The ball will fall at a distance of approximately 22.083 meters from the point of throwing.