A stone dropped from the top of a tower reaches the ground in 3 s. The height of the tower is

Options

A. 18.6 m
B. 39.2 m
C. 44.1 m
D. 98 m

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. Here’s a step-by-step solution:

### Step 1: Identify the known values
- The time taken (t) for the stone to reach the ground is 3 seconds.
- The initial velocity (u) of the stone when dropped is 0 m/s (since it is dropped).
- The acceleration (a) due to gravity is approximately 9.8 m/s².

### Step 2: Use the equation of motion
We can use the second equation of motion, which is:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- \( s \) is the distance traveled (which is the height of the tower, h).
- \( u \) is the initial velocity.
- \( a \) is the acceleration.
- \( t \) is the time taken.

### Step 3: Substitute the known values
Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ s = 0 \cdot t + \frac{1}{2} a t^2 \]
Thus:
\[ h = \frac{1}{2} g t^2 \]
Substituting the values of \( g \) (9.8 m/s²) and \( t \) (3 s):
\[ h = \frac{1}{2} \cdot 9.8 \cdot (3)^2 \]

### Step 4: Calculate the height
Now, calculate \( (3)^2 \):
\[ (3)^2 = 9 \]
Then substitute this back into the equation:
\[ h = \frac{1}{2} \cdot 9.8 \cdot 9 \]
Calculating further:
\[ h = \frac{1}{2} \cdot 88.2 \]
\[ h = 44.1 \, \text{meters} \]

### Final Answer
The height of the tower is **44.1 meters**.

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