Question

Камень бросили с высоты 200 м вертикально вниз.В первую секунду он снижается на 12 м , в каждую следующую секунду проходит на 9,8 м больше,чем в предыдущую.На какой высоте окажется камень через первые 5 с падения?

Answer 1

200-(((12+(12+9,8)+(31,8+9,8)+(41,6+9,8)+51,4)))=21,8

Answer 2

Problem Analysis

We are given that a stone is dropped vertically from a height of 200 m. In the first second, it descends by 12 m, and in each subsequent second, it descends by 9.8 m more than the previous second. We need to determine the height of the stone after 5 seconds of falling.

Solution

To find the height of the stone after 5 seconds, we can calculate the total distance covered by the stone in 5 seconds and subtract it from the initial height of 200 m.

Let's break down the problem into steps:

1. Calculate the total distance covered by the stone in 5 seconds. 2. Subtract the total distance covered from the initial height of 200 m to find the height of the stone after 5 seconds.

Step 1: Calculate the total distance covered by the stone in 5 seconds

To calculate the total distance covered by the stone in 5 seconds, we need to sum up the distances covered in each second.

The distance covered in the first second is 12 m, and in each subsequent second, it increases by 9.8 m.

Let's calculate the total distance covered:

- Distance covered in the first second: 12 m - Distance covered in the second second: 12 m + 9.8 m = 21.8 m - Distance covered in the third second: 21.8 m + 9.8 m = 31.6 m - Distance covered in the fourth second: 31.6 m + 9.8 m = 41.4 m - Distance covered in the fifth second: 41.4 m + 9.8 m = 51.2 m

Therefore, the total distance covered by the stone in 5 seconds is 12 m + 21.8 m + 31.6 m + 41.4 m + 51.2 m = 157 m.

Step 2: Subtract the total distance covered from the initial height

To find the height of the stone after 5 seconds, we subtract the total distance covered (157 m) from the initial height of 200 m.

Height of the stone after 5 seconds = 200 m - 157 m = 43 m.

Answer

The stone will be at a height of 43 meters after the first 5 seconds of falling.