A stone is dropped from the top of a tower. If it hits the ground after 10 seconds, what is the height of the tower?

Explanation

To find the height of the tower from which a stone is dropped and hits the ground after 10 seconds, we can use the equations of motion. Here’s a step-by-step solution:

### Step 1: Identify the known values
- Initial velocity (u) = 0 m/s (since the stone is dropped)
- Time (t) = 10 seconds
- Acceleration due to gravity (g) = 9.8 m/s² (we can approximate this to 10 m/s² for easier calculations)

### Step 2: Use the equation of motion
The equation of motion that relates distance (height in this case), initial velocity, time, and acceleration is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- \( s \) is the distance (height of the tower)
- \( u \) is the initial velocity
- \( a \) is the acceleration (which is \( g \) in this case)
- \( t \) is the time

### Step 3: Substitute the known values into the equation
Since the initial velocity \( u = 0 \):
\[ s = 0 \cdot t + \frac{1}{2} g t^2 \]
This simplifies to:
\[ s = \frac{1}{2} g t^2 \]

### Step 4: Substitute the values of g and t
Using \( g = 10 \, \text{m/s}^2 \) and \( t = 10 \, \text{s} \):
\[ s = \frac{1}{2} \cdot 10 \cdot (10)^2 \]
\[ s = \frac{1}{2} \cdot 10 \cdot 100 \]
\[ s = 5 \cdot 100 \]
\[ s = 500 \, \text{meters} \]

### Step 5: Conclusion
The height of the tower is 500 meters.

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