The 200 m free style women's swimming gold medal at Seol Olympic 1988 went to Heike Friendrich of East Germany when she set a new Olympic record of 1 minute and 57.56 seconds. Assume that she covered most of the distance with a uniform speed and had to exert 460 W to maintain her speed. Calculate the average force of resistance offered by the water during the swim.

Explanation

To solve the problem, we need to find the average force of resistance offered by the water during Heike Friedrich's swim. We will follow these steps:

### Step 1: Convert the time from minutes and seconds to seconds
Heike Friedrich's time for the swim is given as 1 minute and 57.56 seconds. We need to convert this into seconds.

\[ \text{Time in seconds} = 1 \text{ minute} \times 60 \text{ seconds/minute} + 57.56 \text{ seconds} = 60 + 57.56 = 117.56 \text{ seconds} \]

### Step 2: Calculate the work done using power and time
The power exerted by Heike Friedrich is given as 460 Watts. Power is defined as the work done per unit time. Therefore, we can calculate the work done (W) using the formula:

\[ \text{Power} = \frac{W}{T} \implies W = \text{Power} \times T \]

Substituting the values:

\[ W = 460 \text{ W} \times 117.56 \text{ s} = 54077.6 \text{ J} \]

### Step 3: Use the work done to find the average resistive force
The work done is also related to force and displacement by the formula:

\[ W = F \times D \]

Where:
- \( W \) is the work done,
- \( F \) is the average resistive force,
- \( D \) is the displacement (200 m in this case).

Rearranging the formula to find the average resistive force:

\[ F = \frac{W}{D} \]

Substituting the known values:

\[ F = \frac{54077.6 \text{ J}}{200 \text{ m}} = 270.38 \text{ N} \]

### Final Answer
The average force of resistance offered by the water during the swim is approximately **270.38 N**.

---