A particle is dropped from the top of a high building 360 m. The distance travelled by the particle in ninth second is `(g=10 m//s^(2))`

Options

A. 85 m
B. 60 m
C. 40 m
D. can't be determined

Explanation

To find the distance traveled by a particle dropped from a height of 360 meters during the 9th second, we can follow these steps:

### Step 1: Determine the time taken to fall from height h
The time \( t \) taken for an object to fall from a height \( h \) under the influence of gravity \( g \) can be calculated using the formula:

\[ t = \sqrt{\frac{2h}{g}} \]

Given:
- \( h = 360 \, \text{m} \)
- \( g = 10 \, \text{m/s}^2 \)

Substituting the values:

\[ t = \sqrt{\frac{2 \times 360}{10}} = \sqrt{\frac{720}{10}} = \sqrt{72} \approx 8.49 \, \text{s} \]

### Step 2: Calculate the distance traveled in 8 seconds
The distance traveled by the particle in the first \( t \) seconds is given by:

\[ d = \frac{1}{2} g t^2 \]

For \( t = 8 \, \text{s} \):

\[ d = \frac{1}{2} \times 10 \times 8^2 = \frac{1}{2} \times 10 \times 64 = 320 \, \text{m} \]

### Step 3: Calculate the distance traveled in 9 seconds
To find the distance traveled in the 9th second, we need to calculate the distance traveled in 9 seconds and then subtract the distance traveled in the first 8 seconds.

First, calculate the distance traveled in 9 seconds:

\[ d_{9} = \frac{1}{2} g (9^2) = \frac{1}{2} \times 10 \times 81 = 405 \, \text{m} \]

### Step 4: Calculate the distance traveled in the 9th second
The distance traveled during the 9th second is given by:

\[ \text{Distance in 9th second} = d_{9} - d_{8} \]

Substituting the values:

\[ \text{Distance in 9th second} = 405 \, \text{m} - 320 \, \text{m} = 85 \, \text{m} \]

### Final Answer
The distance traveled by the particle in the 9th second is **85 meters**.

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