A body falling from a high mimaret travels 40 meters in the last 2 seconds of its fall to ground. Height of minaret in meters is (take `g=10(m)/(s^2)`)

Options

A. 60
B. 45
C. 80
D. 50

Explanation

To find the height of the minaret from which a body falls, we can use the equations of motion. Let's break down the solution step by step.

### Step 1: Understand the Problem
A body falls from a height and covers 40 meters in the last 2 seconds of its fall. We need to find the total height (H) of the minaret.

### Step 2: Use the Equation of Motion
The distance covered by a freely falling body from rest is given by the equation:
\[ s = ut + \frac{1}{2}gt^2 \]
where:
- \( s \) = distance fallen
- \( u \) = initial velocity (0 m/s, since it starts from rest)
- \( g \) = acceleration due to gravity (10 m/s²)
- \( t \) = time in seconds

### Step 3: Calculate the Distance Fallen in the Last 2 Seconds
Let \( T \) be the total time of fall. The distance fallen in the last 2 seconds can be expressed as:
\[ s_{last} = H - s_{T-2} \]
Where \( s_{T-2} \) is the distance fallen in \( T-2 \) seconds.

Using the equation of motion for the total time \( T \):
\[ H = \frac{1}{2}gT^2 \]
And for \( T-2 \) seconds:
\[ s_{T-2} = \frac{1}{2}g(T-2)^2 \]

### Step 4: Set Up the Equation
From the problem, we know:
\[ H - s_{T-2} = 40 \]
Substituting the equations for \( H \) and \( s_{T-2} \):
\[ \frac{1}{2}gT^2 - \frac{1}{2}g(T-2)^2 = 40 \]

### Step 5: Simplify the Equation
Expanding \( (T-2)^2 \):
\[ (T-2)^2 = T^2 - 4T + 4 \]
Thus,
\[ s_{T-2} = \frac{1}{2}g(T^2 - 4T + 4) \]
Now substituting back:
\[ \frac{1}{2}gT^2 - \frac{1}{2}g(T^2 - 4T + 4) = 40 \]
This simplifies to:
\[ \frac{1}{2}g(4T - 4) = 40 \]
\[ 2g(T - 1) = 40 \]
\[ g(T - 1) = 20 \]

### Step 6: Solve for T
Substituting \( g = 10 \, m/s^2 \):
\[ 10(T - 1) = 20 \]
\[ T - 1 = 2 \]
\[ T = 3 \, seconds \]

### Step 7: Calculate the Height H
Now, substituting \( T \) back into the equation for height:
\[ H = \frac{1}{2}gT^2 \]
\[ H = \frac{1}{2} \times 10 \times (3^2) \]
\[ H = \frac{1}{2} \times 10 \times 9 \]
\[ H = 45 \, meters \]

### Conclusion
The height of the minaret is **45 meters**.

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