A stone dropped from a cliff hits the ground in 4 sec. Height of the cliff is

Options

A. 39.2 m
B. 29.4 m
C. 9.8 m
D. 78.4 m

Answer

To find the height of the cliff 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 (t) it takes for the stone to hit the ground is given as 4 seconds.
- The initial velocity (u) of the stone when it is dropped is 0 m/s (since it is dropped).
- The acceleration (a) due to gravity (g) is approximately 9.8 m/s².

### Step 2: Use the kinematic equation
We will use the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \( s \) is the distance (height of the cliff, h),
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.

### Step 3: Substitute the known values
Since the stone is dropped, we have:
- \( u = 0 \)
- \( a = g = 9.8 \, \text{m/s}^2 \)
- \( t = 4 \, \text{s} \)

Substituting these values into the equation:
\[ h = 0 \cdot t + \frac{1}{2} g t^2 \]

### Step 4: Simplify the equation
Since \( u = 0 \), the equation simplifies to:
\[ h = \frac{1}{2} g t^2 \]

### Step 5: Calculate the height
Now substituting the values of \( g \) and \( t \):
\[ h = \frac{1}{2} \cdot 9.8 \cdot (4^2) \]
\[ h = \frac{1}{2} \cdot 9.8 \cdot 16 \]
\[ h = 4.9 \cdot 16 \]
\[ h = 78.4 \, \text{meters} \]

### Conclusion
The height of the cliff is **78.4 meters**.

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