A 62 kg person, standing on a diving board, dives straight down into the water. Just before striking the water, her speed is 5.50 m/s. At a time of 1.65 s after she enters the water, her speed is reduced to 1.10 m/s. What is the net average force (magnitude and direction) that acts on her when she is in the water?

Options

A. 206 N, downward
B. 248 N, upward
C. 248 N, downward
D. 165 N, upward

Answer

To solve the problem, we need to calculate the net average force acting on the person when she is in the water. We will use the formula for average force, which is derived from the change in momentum over time.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the person (m) = 62 kg
- Initial speed just before entering the water (u) = 5.50 m/s
- Final speed after 1.65 seconds in the water (v) = 1.10 m/s
- Time interval (Δt) = 1.65 s

2. **Calculate the Initial Momentum (p_initial):**
\[ p_{\text{initial}} = m \cdot u = 62 \, \text{kg} \cdot 5.50 \, \text{m/s} = 341 \, \text{kg m/s} \]

3. **Calculate the Final Momentum (p_final):**
\[ p_{\text{final}} = m \cdot v = 62 \, \text{kg} \cdot 1.10 \, \text{m/s} = 68.2 \, \text{kg m/s} \]

4. **Calculate the Change in Momentum (Δp):**
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} = 68.2 \, \text{kg m/s} - 341 \, \text{kg m/s} = -272.8 \, \text{kg m/s} \]

5. **Calculate the Average Force (F_avg):**
The average force can be calculated using the formula:
\[ F_{\text{avg}} = \frac{\Delta p}{\Delta t} = \frac{-272.8 \, \text{kg m/s}}{1.65 \, \text{s}} \approx -165.03 \, \text{N} \]

6. **Determine the Direction of the Force:**
The negative sign indicates that the force is acting in the opposite direction to the motion of the person. Since the person is moving downwards, the average force exerted by the water is upwards.

### Final Answer:
The net average force acting on the person while she is in the water is approximately **165 N upwards**.

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