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 determine how high the athlete can jump, we need to calculate the gravitational potential energy (GPE) that can be obtained from the food consumed.
First, let's calculate the energy converted from the meal:
Energy from food = 4.00 * 10^3 kcal
Next, we need to find the energy that can be converted to gravitational potential energy. Given that only 3.3% of the energy can be converted, we can calculate:
Energy converted = (3.3/100) * Energy from food
Now, let's calculate the gravitational potential energy using the formula:
GPE = m * g * h
where:
m = mass of the athlete = 80.0 kg
g = acceleration due to gravity = 9.8 m/s^2 (standard value)
h = maximum height (unknown)
Setting the energy converted equal to the gravitational potential energy, we have:
Energy converted = GPE
Substituting the values:
(3.3/100) * Energy from food = m * g * h
Rearranging the equation, we can solve for h:
h = (Energy converted) / (m * g)
Plugging in the values, we get:
h = ((3.3/100) * Energy from food) / (m * g)
Now, let's calculate the maximum height:
h = ((3.3/100) * 4.00 * 10^3 kcal) / (80.0 kg * 9.8 m/s^2)
Calculating this expression, we get:
h ≈ 17.95 meters
Therefore, the athlete can jump approximately 17.95 meters high.