We are asked to analyze the change in momentum of a ball that bounces off the floor, with the following known information:

• Mass of the ball: $m = 275 \, \text{g} = 0.275 \, \text{kg}$
• Speed before hitting the floor: $v_{\text{initial}} = 2.30 \, \text{m/s}$
• Speed after rebounding: $v_{\text{final}} = 1.70 \, \text{m/s}$
• The upward direction is defined as positive.

We will compute:

(a) The magnitude of the change in the ball's momentum (Δp):

Momentum is given by $p = m \times v$. The change in momentum $\Delta p$ is the difference between the final and initial momentum, taking into account direction (since the velocities are in opposite directions):

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

Given that the final velocity is upward (positive) and the initial velocity is downward (negative, since it's the opposite direction):

$\Delta p = 0.275 \times (1.70) - 0.275 \times (-2.30)$ $\Delta p = 0.275 \times (1.70 + 2.30)$ $\Delta p = 0.275 \times 4.00 = 1.10 \, \text{kg·m/s}$

So, the magnitude of the change in momentum is:

$\boxed{1.10 \, \text{kg·m/s}}$

(b) The change in the magnitude of the ball's momentum:

Here, we only consider the magnitudes of the velocities (ignoring direction). The change in magnitude is the absolute difference between the final and initial momentum magnitudes:

$\Delta p_{\text{magnitude}} = m \times \left| v_{\text{final}} - v_{\text{initial}} \right|$

$\Delta p_{\text{magnitude}} = 0.275 \times \left| 1.70 - 2.30 \right|$ $\Delta p_{\text{magnitude}} = 0.275 \times 0.60 = 0.165 \, \text{kg·m/s}$

So, the change in the magnitude of the ball's momentum is:

$\boxed{0.165 \, \text{kg·m/s}}$

(c) Which of the two quantities is more directly related to the net force acting on the ball?

The net force acting on the ball during the collision is related to the magnitude of the change in the ball's momentum because force is defined by the impulse-momentum theorem:

$F \Delta t = \Delta p$

Thus, the force is directly proportional to the total change in momentum (not just the magnitude of the change in momentum).

Therefore, the correct answer is:

$\boxed{\text{the magnitude of the change in the ball's momentum}}$

Do you need any clarifications or further details? Here are some related questions:

1. How does the direction of velocity affect momentum changes?
2. What is the impulse-momentum theorem and how does it apply here?
3. How would the result change if the ball was inelastic and didn't bounce back?
4. What is the significance of the sign of momentum in physics problems?
5. How does this problem relate to Newton's third law?

Tip: Always pay attention to the sign of velocities when calculating momentum changes, as direction plays a critical role in momentum conservation problems.