A stone is dropped from the top if a cliff and is found to travel ` 44. 1m` in the last second before it reaches the ground . Fing the height of the cliff.

Options

A. `100`
B. `122.5`
C. `150`
D. `200`

Explanation

To solve the problem of finding the height of the cliff from which a stone is dropped, we will follow these steps:

### Step 1: Understand the problem
A stone is dropped from the top of a cliff and travels a distance of 44.1 m in the last second before it hits the ground. We need to find the total height of the cliff.

### Step 2: Use the formula for distance traveled in the last second
The distance traveled in the last second can be expressed using the formula:
\[ S = U + \frac{A}{2} \cdot (2N - 1) \]
where:
- \( S \) is the distance traveled in the last second (44.1 m),
- \( U \) is the initial velocity (0 m/s since the stone is dropped),
- \( A \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( N \) is the total time in seconds.

### Step 3: Set up the equation
Substituting the known values into the formula:
\[ 44.1 = 0 + \frac{9.8}{2} \cdot (2N - 1) \]
This simplifies to:
\[ 44.1 = 4.9 \cdot (2N - 1) \]

### Step 4: Solve for \( N \)
Now, we can solve for \( N \):
\[ 44.1 = 4.9 \cdot (2N - 1) \]
\[ 2N - 1 = \frac{44.1}{4.9} \]
\[ 2N - 1 = 9 \]
\[ 2N = 10 \]
\[ N = 5 \]

### Step 5: Calculate the height of the cliff
Now that we know the total time \( N \) is 5 seconds, we can find the height of the cliff using the formula:
\[ H = U \cdot T + \frac{1}{2} A T^2 \]
Substituting the values:
\[ H = 0 \cdot 5 + \frac{1}{2} \cdot 9.8 \cdot (5^2) \]
\[ H = 0 + \frac{1}{2} \cdot 9.8 \cdot 25 \]
\[ H = 4.9 \cdot 25 \]
\[ H = 122.5 \, \text{m} \]

### Conclusion
The height of the cliff is **122.5 meters**.

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