A high jumper of mass 80.0 kg consumes a meal of 4.00 103 kcal prior to a jump. If 3.3% of the energy from the food could be converted to gravitational potential energy in a single jump, how high could the athlete jump?

To calculate the height the athlete could jump, we need to determine the converted gravitational potential energy.

1. Find the total energy consumed by the athlete. We know the energy from the food is 4.00 * 10^3 kcal.

2. Convert the kcal to joules: 1 kcal = 4184 J.

Total Energy Consumed = 4.00 * 10^3 kcal * 4184 J/kcal.

3. Calculate the converted energy that can be converted to gravitational potential energy:

Converted Energy = Total Energy Consumed * Conversion Efficiency.
(Conversion Efficiency is given as 3.3%, which can be written as 3.3/100 = 0.033)

4. Determine the gravitational potential energy using the formula:

Gravitational Potential Energy = mass * gravity * height.

We know the mass of the high jumper is 80.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2.

Gravitational Potential Energy = Converted Energy.

5. Rearrange the formula to solve for height:

height = Converted Energy / (mass * gravity).

Now, let's calculate the height the athlete could jump:

Step 1:
Total Energy Consumed = 4.00 * 10^3 kcal * 4184 J/kcal = 16.736 * 10^6 J.

Step 2:
Converted Energy = Total Energy Consumed * Conversion Efficiency = 16.736 * 10^6 J * 0.033 = 551.088 * 10^3 J.

Step 3:
Gravitational Potential Energy = Converted Energy = 551.088 * 10^3 J.

Step 4:
height = Gravitational Potential Energy / (mass * gravity) = 551.088 * 10^3 J / (80.0 kg * 9.8 m/s^2).

Step 5:
height = 710.52 m.

Therefore, the athlete could potentially jump approximately 710.52 meters high.

To calculate the height the athlete can jump, we need to determine the amount of energy that can be converted to gravitational potential energy and then use the formula for gravitational potential energy.

Step 1: Convert the energy from kcal to Joules
1 kcal is equal to 4184 Joules.
So, the energy consumed by the athlete can be converted to Joules by multiplying 4.00 x 10^3 kcal by 4184 J/kcal.

Energy consumed = 4.00 x 10^3 kcal * 4184 J/kcal.

Step 2: Calculate the amount of energy that can be converted to gravitational potential energy.
From the problem, it is given that 3.3% of the energy can be converted to gravitational potential energy.
So, we can calculate the gravitational potential energy by multiplying the total energy consumed by 3.3%.

Gravitational potential energy = Energy consumed * 0.033

Step 3: Calculate the height using gravitational potential energy formula.
The formula for gravitational potential energy is:

Gravitational potential energy (PE) = mgh

Where:
m = mass (in kg)
g = acceleration due to gravity (9.8 m/s^2 on Earth)
h = height (in meters)

We can rearrange the formula to solve for h:

h = PE / (mg)

Step 4: Substitute the values into the formula and calculate the height.
Substituting the values into the formula:

h = (Gravitational potential energy) / (mass * acceleration due to gravity)

h = (Gravitational potential energy) / (80.0 kg * 9.8 m/s^2)

Now, let's plug in the values and calculate the height.