A cement block accidentally falls from rest from the ledge of a 63-m-high building. When the block is 14.0 m above the ground, a man, 2.00 m tall, looks up and notices that the block is directly above him. How much time, at most, does the man have to get out of the way?

We can solve this problem by using the equations of motion under constant acceleration due to gravity.

### Given:
- Initial height of the block: \( h_0 = 63 \, \text{m} \)
- Final height (when the block is 14.0 m above the ground): \( h = 14.0 \, \text{m} \)
- Acceleration due to gravity: \( g = 9.8 \, \text{m/s}^2 \)
- The block starts from rest: \( v_0 = 0 \)

We need to find how much time, \( t \), the man has before the block reaches the ground. The height above the ground where the man notices the block is \( h = 14.0 \, \text{m} \).

### Step 1: Use the equation of motion to find the time from 14 m to 0 m.

The general equation of motion for vertical displacement under gravity is:
\[
h = h_0 + v_0 t - \frac{1}{2} g t^2
\]
Since \( v_0 = 0 \) (the block falls from rest), the equation simplifies to:
\[
h = h_0 - \frac{1}{2} g t^2
\]

To calculate the time, we can rearrange the equation to isolate \( t \):
\[
t = \sqrt{\frac{2(h_0 - h)}{g}}
\]
Substituting the values:
\[
t = \sqrt{\frac{2(14.0 \, \text{m} - 0 \, \text{m})}{9.8 \, \text{m/s}^2}}
\]
Let me calculate this for you.The man has approximately **1.69 seconds** to get out of the way before the block reaches the ground.

Would you like further details or clarifications on any part of the solution?

Here are 5 related questions to expand your understanding:
1. How would the problem change if the man were taller or shorter?
2. What if the block had an initial velocity, not zero? How would we solve it?
3. How can we calculate the velocity of the block when it is 14 meters above the ground?
4. How long would it take for the block to fall from the top of the building to the ground?
5. What role does air resistance play in a real-life situation like this?

**Tip:** In free-fall problems, always check if the initial velocity is zero, which simplifies calculations significantly.

Solve a physics problem involving a falling cement block from a height of 63 meters. Learn how to calculate the time it takes for the block to hit the ground using the equations of motion under constant acceleration. Suitable for high school students in Grades 9-12.

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