As athlete in the olympic ganes cover a distance of `100 m` in `10 s`. Hiskinetic energy can be estrimated to be in the range : (Take mass= 60 kg approx.)

Options

A. `200 J - 500 J`
B. `2 xx 10^(5) J -3 xx 10^(5)J`
C. `20,000 J - 50,000 J`
D. `2,000 J - 5,000 J`

Answer

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

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

### Step 2: Use the Kinetic Energy Formula
The kinetic energy (KE) of an object 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 speed of the athlete (10 m/s)

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

### Step 4: Determine the Range of Kinetic Energy
The calculated kinetic energy is 3000 Joules. According to the options provided, we need to find the range in which this value lies. The options suggest that the kinetic energy lies between 2000 to 5000 Joules.

### Conclusion
Thus, the estimated kinetic energy of the athlete is approximately 3000 Joules, which falls within the specified range of 2000 to 5000 Joules.

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