The US athlete Florence Griffith oyner won the 100 m spring gold medal at Seol Olympic 1988 setting a new Olympic record of 10.54s. Assume that she achieved her maximum speed in a very short time and then ran the race with that speed till she crossed the line. Take her mas ot be 50 kg. a. Calculate the kinetic energy of Griffith Joyner at her full speed. b. Assuming tht the track the wind etc. offered an average resistance of one tenth of her weight, cfalculate the work done by the resistsnce durng the run. c. What power Griffith Joyner had to exet ot maintain uniform speed?

Explanation

To solve the problem step by step, we will break it down into three parts as outlined in the question.

### Part a: Calculate the kinetic energy of Griffith Joyner at her full speed.

1. **Determine the velocity**:
The distance covered is 100 meters and the time taken is 10.54 seconds.
\[ \text{Velocity} (v) = \frac{\text{Distance}}{\text{Time}} = \frac{100 \, \text{m}}{10.54 \, \text{s}} \approx 9.5 \, \text{m/s} \]

2. **Calculate the kinetic energy**:
The formula for kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass (50 kg) and \( v \) is the velocity (9.5 m/s).
\[ KE = \frac{1}{2} \times 50 \, \text{kg} \times (9.5 \, \text{m/s})^2 \]
\[ KE = 25 \times 90.25 \approx 2256.25 \, \text{J} \]

### Part b: Calculate the work done by the resistance during the run.

1. **Determine the average resistance force**:
The average resistance is given as one-tenth of her weight.
\[ \text{Weight} = m \times g = 50 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 490 \, \text{N} \]
\[ \text{Resistance force} (R) = \frac{1}{10} \times 490 \, \text{N} = 49 \, \text{N} \]

2. **Calculate the work done by the resistance**:
Work done (W) by the resistance is given by:
\[ W = -R \times d \]
where \( d \) is the distance (100 m).
\[ W = -49 \, \text{N} \times 100 \, \text{m} = -4900 \, \text{J} \]

### Part c: Calculate the power Griffith Joyner had to exert to maintain uniform speed.

1. **Calculate the power**:
Power (P) is given by the formula:
\[ P = F \times v \]
where \( F \) is the force exerted to overcome the resistance (which is equal to the resistance force) and \( v \) is the velocity.
\[ P = R \times v = 49 \, \text{N} \times 9.5 \, \text{m/s} \]
\[ P \approx 465.5 \, \text{W} \]

### Summary of Results:
- a. Kinetic Energy: \( \approx 2256.25 \, \text{J} \)
- b. Work done by resistance: \( -4900 \, \text{J} \)
- c. Power exerted: \( \approx 465.5 \, \text{W} \)