A ball rolls off of a 1.41-meter-high table and lands 0.61 meters from the base of the table. How fast (in m/s) was the ball rolling, rounded to one decimal place?

To solve this problem, we need to determine the horizontal velocity of the ball as it rolls off the table.

### Step 1: Calculate the time of flight
The time it takes for the ball to hit the ground is determined by the height of the table. We use the following kinematic equation for free fall:

\[
h = \frac{1}{2} g t^2
\]

Where:
- \( h = 1.41 \, \text{meters} \) (height of the table)
- \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( t \) is the time in seconds.

Rearrange the equation to solve for \( t \):

\[
t = \sqrt{\frac{2h}{g}}
\]

\[
t = \sqrt{\frac{2 \times 1.41}{9.81}} \approx \sqrt{0.287} \approx 0.536 \, \text{seconds}
\]

### Step 2: Calculate the horizontal velocity
The horizontal distance traveled by the ball is given as 0.61 meters. The horizontal velocity \( v \) is found using the equation:

\[
v = \frac{d}{t}
\]

Where:
- \( d = 0.61 \, \text{meters} \) (horizontal distance)
- \( t = 0.536 \, \text{seconds} \) (time calculated above)

Substitute the values:

\[
v = \frac{0.61}{0.536} \approx 1.138 \, \text{m/s}
\]

### Step 3: Round the velocity to one decimal place

\[
v \approx 1.1 \, \text{m/s}
\]

So, the ball was rolling at a speed of **1.1 m/s**.

Would you like a detailed explanation of any part of this solution? Here are five related questions:

1. How does the height of the table affect the time of flight?
2. What if the ball was rolling faster? How would the horizontal distance change?
3. How does air resistance affect the motion of the ball?
4. Can this problem be solved using energy conservation principles?
5. How would the solution differ if the ball were rolling off a sloped surface?

**Tip:** When dealing with projectile motion, separate the vertical and horizontal components of the motion.

Learn how to calculate the horizontal velocity of a ball rolling off a 1.41-meter-high table and landing 0.61 meters away from the base. Understand the application of projectile motion and kinematic equations in solving this problem. Suitable for Grades 10-12.

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