To solve this problem, let's break it down into two parts.

1. Impulse Acting on the Ball

Impulse is defined as the change in momentum of an object. The momentum $p$ is the product of mass and velocity:

$p = m \cdot v$

The impulse $J$ is given by the formula:

$J = \Delta p = m \cdot v_{\text{final}} - m \cdot v_{\text{initial}}$

Where:

• $m = 1.77 \, \text{kg}$ (mass of the ball),
• $v_{\text{initial}} = -33.2 \, \text{m/s}$ (velocity just before hitting the floor, negative because it's downward),
• $v_{\text{final}} = 5.38 \, \text{m/s}$ (velocity just after rebounding, positive because it's upward).

Now, let's calculate the impulse:

$J = 1.77 \, \text{kg} \cdot (5.38 \, \text{m/s} - (-33.2 \, \text{m/s}))$

$J = 1.77 \cdot (5.38 + 33.2) = 1.77 \cdot 38.58$

$J \approx 68.3 \, \text{Ns}$

So, the impulse acting on the ball is approximately 68.3 Ns.

2. Average Force on the Floor from the Ball

The average force $F_{\text{avg}}$ is related to impulse and the time of contact by the following formula:

$F_{\text{avg}} = \frac{J}{\Delta t}$

Where:

• $J = 68.3 \, \text{Ns}$ (impulse),
• $\Delta t = 0.0222 \, \text{s}$ (time of contact with the floor).

Now, calculating the average force:

$F_{\text{avg}} = \frac{68.3}{0.0222}$

$F_{\text{avg}} \approx 3076.57 \, \text{N}$

So, the magnitude of the average force on the floor from the ball is approximately 3077 N.

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Would you like more details on the calculations or any further explanations?

Here are some related questions you might find useful:

1. What factors affect the impulse experienced by an object?
2. How does the time of contact influence the average force?
3. How can we calculate the change in kinetic energy during this rebound?
4. What would happen if the ball hit the floor with a higher or lower initial velocity?
5. How does the direction of velocity impact the calculation of impulse and force?

Tip: When dealing with impulse problems, remember that the sign convention is important: downward velocities are typically negative, while upward velocities are positive.