Question

Завдання 5. Аеростат піднімається з землi вертикально вгору з прискоренням 2.45м/с2. Через 8 секунд від початку руху з його гондоли випадає предмет. Через скільки часу і з якою швидкістю цей предмет впаде на землю? Опором повітря знехтувати.​

Answer 1

Problem Analysis

We are given that a balloon is ascending vertically with an acceleration of 2.45 m/s^2. After 8 seconds, an object falls from the gondola of the balloon. We need to determine the time it takes for the object to fall to the ground and its final velocity. We can assume that air resistance is negligible.

Solution

To solve this problem, we can use the equations of motion for vertical motion under constant acceleration. The equations we will use are:

1. Final velocity equation: v = u + at 2. Displacement equation: s = ut + (1/2)at^2 3. Final velocity squared equation: v^2 = u^2 + 2as

Where: - v is the final velocity - u is the initial velocity (which is 0 in this case, as the object falls from rest) - a is the acceleration (which is -9.8 m/s^2, taking into account the acceleration due to gravity) - t is the time - s is the displacement

Let's solve the problem step by step.

Step 1: Calculate the time it takes for the object to fall to the ground. Given: - Initial velocity (u) = 0 m/s - Acceleration (a) = -9.8 m/s^2 (taking into account the acceleration due to gravity) - Displacement (s) = unknown (we need to find this)

Using the displacement equation, we can rearrange it to solve for time (t): s = ut + (1/2)at^2 Rearranging the equation: (1/2)at^2 + ut - s = 0

Substituting the given values: (1/2)(-9.8)t^2 + 0t - s = 0

Since the object falls to the ground, the displacement (s) is equal to 0. Therefore, the equation becomes: (1/2)(-9.8)t^2 = 0

Simplifying the equation: -4.9t^2 = 0

Since the coefficient of t^2 is 0, the equation becomes: 0 = 0

This equation is true for all values of t. Therefore, the time it takes for the object to fall to the ground is not determined by the given information. We need additional information to solve for the time.

Step 2: Calculate the final velocity of the object when it hits the ground. Given: - Initial velocity (u) = 0 m/s - Acceleration (a) = -9.8 m/s^2 (taking into account the acceleration due to gravity) - Time (t) = 8 s - Final velocity (v) = unknown (we need to find this)

Using the final velocity equation: v = u + at

Substituting the given values: v = 0 + (-9.8)(8) v = -78.4 m/s

Therefore, the final velocity of the object when it hits the ground is -78.4 m/s.

In conclusion, we have determined that the time it takes for the object to fall to the ground is not determined by the given information. However, the final velocity of the object when it hits the ground is -78.4 m/s.