To solve the problem, we will analyze the situation step by step.
### Step 1: Understanding the Problem
We have two balls, A and B, both with mass \( m \). Ball B is at rest on a table that is 5 meters high. Ball A is moving and collides elastically with ball B, causing ball B to remain at rest and ball A to slide off the table.
### Step 2: Determine the Velocity of Ball A Before Collision
Since the collision is elastic and both balls have the same mass, we can use the conservation of momentum and kinetic energy. After the collision, ball A will move with the same velocity that ball B had before the collision.
Using the conservation of energy:
\[
\frac{1}{2} m v^2 = mgh
\]
Where:
- \( h = 5 \, \text{m} \)
- \( g = 10 \, \text{m/s}^2 \)
Rearranging gives:
\[
v^2 = 2gh
\]
Substituting the values:
\[
v^2 = 2 \times 10 \times 5 = 100
\]
Taking the square root:
\[
v = \sqrt{100} = 10 \, \text{m/s}
\]
Thus, the velocity of ball A before the collision is \( 10 \, \text{m/s} \).
### Step 3: Analyzing the Motion of Ball A After Collision
After the collision, ball A slides off the table horizontally. We need to find the time it takes for ball A to hit the ground.
Using the formula for the time of free fall:
\[
h = \frac{1}{2} g t^2
\]
Substituting \( h = 5 \, \text{m} \) and \( g = 10 \, \text{m/s}^2 \):
\[
5 = \frac{1}{2} \times 10 \times t^2
\]
This simplifies to:
\[
5 = 5t^2 \implies t^2 = 1 \implies t = 1 \, \text{s}
\]
### Step 4: Finding the Horizontal Distance
Now, we can calculate the horizontal distance traveled by ball A while it is falling. The horizontal distance \( d \) can be calculated using:
\[
d = v \times t
\]
Where:
- \( v = 10 \, \text{m/s} \)
- \( t = 1 \, \text{s} \)
Substituting the values:
\[
d = 10 \times 1 = 10 \, \text{m}
\]
### Step 5: Conclusion
The horizontal distance from the table to where ball A strikes the ground is indeed \( 10 \, \text{m} \), which matches the information provided in the problem.
### Final Answers
1. The velocity of ball A before the collision is \( 10 \, \text{m/s} \).
2. The time taken for ball A to hit the ground is \( 1 \, \text{s} \).
3. The horizontal distance traveled by ball A is \( 10 \, \text{m} \).
