Let's solve the problem step by step to find the horizontal velocity of the ball as it rolls off the table.

Step 1: Determine the time of flight

The ball falls freely under the influence of gravity. We use the following equation to calculate the time $t$ it takes to hit the ground:

$h = \frac{1}{2} g t^2$

Where:

• $h = 1.41 \, \text{meters}$ (height of the table)
• $g = 9.81 \, \text{m/s}^2$ (acceleration due to gravity)

Rearrange the equation to solve for $t$:

$t = \sqrt{\frac{2h}{g}}$

Substitute the values:

$t = \sqrt{\frac{2 \times 1.41}{9.81}} = \sqrt{\frac{2.82}{9.81}} \approx \sqrt{0.287} \approx 0.536 \, \text{seconds}$

Step 2: Calculate the horizontal velocity

The horizontal distance $d$ the ball travels is 0.61 meters. The horizontal velocity $v$ is given by:

$v = \frac{d}{t}$

Substitute the known values:

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

Step 3: Round to one decimal place

$v \approx 1.1 \, \text{m/s}$

Final Answer

The ball was rolling at a speed of 1.1 m/s.

Do you need further explanation or details? Here are five related questions:

1. How would the problem change if the table height were doubled?
2. What would happen if the ball was thrown horizontally with an initial speed?
3. How does gravity influence the horizontal motion of the ball?
4. What is the significance of ignoring air resistance in this problem?
5. How could you use this calculation in a real-world scenario?

Tip: Always check your units and rounding at the final step to ensure accuracy in your results.