Question

Мяч падает с высоты 2м и после удара о пол поднимается на высоту 1.5 м. Чему равны путь мяча за все время движения и модуль его перемещения?! ПОМОГИТЕ ПОЖАЛУЙСТА:*

Answer 1

Путь равен длине всей траектории движения:
L = 2 + 1,5 = 3,5 м
Модуль перемещения равен расстоянию от начальной точки до конечной (часто не совпадает с величиной пути!)
|S| = 2 - 1,5 = 0,5 м.

Answer 2

Calculation of the Ball's Path and Displacement

To calculate the path and displacement of the ball, we can use the equations of motion. Let's break down the problem step by step.

Given: - Initial height (h1) = 2m - Final height (h2) = 1.5m

To find the path covered by the ball, we need to calculate the total distance traveled by the ball during its motion.

1. First, let's calculate the time taken by the ball to reach the ground from the initial height (h1).

We can use the equation of motion for vertical motion:

h = ut + (1/2)gt^2

where: - h is the height - u is the initial velocity (which is 0 in this case, as the ball is dropped) - g is the acceleration due to gravity (approximately 9.8 m/s^2) - t is the time

Plugging in the values: 2 = 0*t + (1/2)*9.8*t^2

Solving this equation will give us the time taken by the ball to reach the ground.

2. Once we have the time taken to reach the ground, we can calculate the total time of flight (T) for the ball.

The total time of flight is twice the time taken to reach the ground, as the ball will take the same amount of time to go up and down.

3. Now, let's calculate the maximum height (h_max) reached by the ball after bouncing off the ground.

We can use the equation of motion for vertical motion:

v^2 = u^2 + 2gh

where: - v is the final velocity (which is 0 when the ball reaches the maximum height) - u is the initial velocity (which is the velocity just before the ball hits the ground) - g is the acceleration due to gravity (approximately 9.8 m/s^2) - h is the maximum height

Plugging in the values: 0 = u^2 + 2*9.8*h_max

Solving this equation will give us the maximum height reached by the ball.

4. Finally, we can calculate the total distance traveled by the ball during its motion.

The total distance traveled is the sum of the distances covered during the upward and downward motions.

- The distance covered during the upward motion is the difference between the initial height (h1) and the maximum height (h_max). - The distance covered during the downward motion is the difference between the maximum height (h_max) and the final height (h2).

Adding these two distances will give us the total distance traveled by the ball.

5. The displacement of the ball is the difference between the initial position and the final position.

The initial position is the initial height (h1), and the final position is the final height (h2).

Now, let's calculate the values step by step using the given information.

Calculation Steps:

1. Calculate the time taken to reach the ground: - Using the equation h = ut + (1/2)gt^2, where h = 2m and g = 9.8 m/s^2, we can solve for t. - Plugging in the values, we get: 2 = 0*t + (1/2)*9.8*t^2 - Solving this equation, we find that t ≈ 0.64 seconds.

2. Calculate the total time of flight: - The total time of flight (T) is twice the time taken to reach the ground. - Therefore, T = 2 * t ≈ 2 * 0.64 ≈ 1.28 seconds.

3. Calculate