A stone released with zero velocity from the top of a water, reaches the ground in 4s. The height of the tower is `(g = 10 m//s^(2))`

Options

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

Answer

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

### Step 1: Identify the given values
- Initial velocity (u) = 0 m/s (since the stone is released)
- Time (t) = 4 s
- Acceleration (a) = g = 10 m/s² (acceleration due to gravity)

### Step 2: Use the equation of motion
We can use the second equation of motion which relates displacement (height in this case), initial velocity, time, and acceleration:
\[ h = ut + \frac{1}{2} a t^2 \]

### Step 3: Substitute the known values
Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ h = 0 \cdot t + \frac{1}{2} a t^2 \]
\[ h = \frac{1}{2} (10) (4^2) \]

### Step 4: Calculate \( t^2 \)
Calculate \( t^2 \):
\[ t^2 = 4^2 = 16 \]

### Step 5: Substitute \( t^2 \) back into the equation
Now substitute \( t^2 \) back into the equation for height:
\[ h = \frac{1}{2} \cdot 10 \cdot 16 \]

### Step 6: Perform the multiplication
Calculate the height:
\[ h = \frac{1}{2} \cdot 10 \cdot 16 = 5 \cdot 16 = 80 \text{ m} \]

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

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