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Chapter 14: Problem 15

A high jumper of mass \(60.0 \mathrm{kg}\) consumes a meal of $3.00 \times 10^{3} \mathrm{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?

Short Answer

Expert verified
Answer: The high jumper can jump approximately 6.96 meters high.

Step by step solution

01

Convert Kcal to Joules

We need to convert the energy given in Kcal to Joules. We know that 1 Kcal = 4184 Joules. So, we have: Energy in Joules = Energy in Kcal * conversion factor Energy in Joules = 3000 Kcal * 4184 J/Kcal = 12,552,000 J
02

Find the converted gravitational potential energy

We are given that 3.3% of the energy from the food can be converted into GPE. So, we have: Converted GPE = Total energy * percentage converted Converted GPE = 12,552,000 J * 0.033 = 414216 J
03

Find the height the athlete could jump

We use the gravitational potential energy formula, GPE = m * g * h, where m is the mass (60 kg), g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height in meters. Rearranging the formula for h, we get: h = GPE / (m * g) h = 414216 J / (60 kg * 9.81 m/s²) h ≈ 6.96 m So, the athlete could jump approximately 6.96 meters high.

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