An Athlete in the Olympic games covers a distance of 100 m in 10s, this kinetic eneryg can be estimated to be in the range (assume `m=60kg`)

Options

A. 200J-500J
B. `2xx10^(5)J-3xx10^(5)j`
C. `20000J-50000J`
D. `2000J-5000J`

Explanation

To solve the problem of estimating the kinetic energy of an athlete who covers a distance of 100 m in 10 seconds with a mass of 60 kg, we can follow these steps:

### Step 1: Calculate the average velocity of the athlete.
The average velocity (v) can be calculated using the formula:
\[ v = \frac{\text{distance}}{\text{time}} \]
Given that the distance is 100 m and the time is 10 s:
\[ v = \frac{100 \, \text{m}}{10 \, \text{s}} = 10 \, \text{m/s} \]

### Step 2: Use the kinetic energy formula.
The kinetic energy (KE) can be calculated using the formula:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( m \) is the mass of the athlete (60 kg)
- \( v \) is the average velocity (10 m/s)

### Step 3: Substitute the values into the kinetic energy formula.
Substituting the values we have:
\[ KE = \frac{1}{2} \times 60 \, \text{kg} \times (10 \, \text{m/s})^2 \]
Calculating \( (10 \, \text{m/s})^2 \):
\[ (10 \, \text{m/s})^2 = 100 \, \text{m}^2/\text{s}^2 \]
Now substituting back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 60 \times 100 \]
\[ KE = 30 \times 100 = 3000 \, \text{Joules} \]

### Step 4: Determine the range of the kinetic energy.
Now that we have calculated the kinetic energy to be 3000 Joules, we need to check which range this value falls into.

- The options provided are:
1. 200 to 500 Joules
2. 2000 to 3000 Joules
3. 20000 to 50000 Joules
4. 2000 to 5000 Joules

Since 3000 Joules falls within the range of 2000 to 5000 Joules, the correct answer is option 4.

### Final Answer:
The kinetic energy of the athlete is approximately 3000 Joules, which falls within the range of 2000 to 5000 Joules.

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