A stone dropped from the top of the tower touches the ground in 4 sec. The height of the tower is about

Options

A. 80 m
B. 40m
C. 20m
D. 160m

Answer

To solve the problem of finding the height of the tower from which a stone is dropped, we can use the equations of motion under uniform acceleration. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a stone that is dropped from the top of a tower and it takes 4 seconds to reach the ground. We need to find the height of the tower.

### Step 2: Identify Known Values
- Time (T) = 4 seconds
- Initial velocity (u) = 0 m/s (since the stone is dropped)
- Acceleration (a) = g = 10 m/s² (approximately, for simplicity)

### Step 3: Use the Second Equation of Motion
The second equation of motion is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- \( s \) is the distance traveled (height of the tower, H)
- \( u \) is the initial velocity
- \( a \) is the acceleration
- \( t \) is the time taken

### Step 4: Substitute Known Values
Since the initial velocity \( u = 0 \):
\[ H = 0 \cdot T + \frac{1}{2} g T^2 \]
Substituting the values:
\[ H = \frac{1}{2} \cdot 10 \cdot (4)^2 \]

### Step 5: Calculate the Height
Now calculate \( (4)^2 \):
\[ (4)^2 = 16 \]
Now substitute this back into the equation:
\[ H = \frac{1}{2} \cdot 10 \cdot 16 \]
\[ H = 5 \cdot 16 \]
\[ H = 80 \text{ meters} \]

### Conclusion
The height of the tower is approximately **80 meters**.

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