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Chapter 4: Problem 128

An athlete in the Olympic Games covers a distance of \(100 \mathrm{~m}\) in \(10 \mathrm{~s}\). His kinetic energy can be estimated to be in the range [2008] (A) \(200 \mathrm{~J}-500 \mathrm{~J}\) (B) \(2 \times 10^{5} \mathrm{~J}-3 \times 10^{5} \mathrm{~J}\) (C) \(20,000 \mathrm{~J}-50,000 \mathrm{~J}\) (D) \(2,000 \mathrm{~J}-5,000 \mathrm{~J}\)

Short Answer

Expert verified
The athlete's kinetic energy is estimated to be in the range (D) 2,000 J - 5,000 J.

Step by step solution

01

Calculate the velocity of the athlete

To find the athlete's velocity, we'll use the formula: velocity = distance / time. The distance covered is 100 meters, and the time taken is 10 seconds. So, the velocity is 10 meters per second (m/s).
02

Estimate the athlete's mass

Although the mass of the athlete is not given, we can estimate it to be around 70 kg since this is an average mass for an adult male.
03

Calculate the kinetic energy

With the estimated mass of 70 kg and a velocity of 10 m/s, we can now calculate the athlete's kinetic energy (KE) using the formula KE = 0.5 * m * v^2: \(KE = 0.5 * 70 \text{ kg} * (10 \text{ m/s})^2 = 0.5 * 70 * 100 = 3500 \text{ J}\).
04

Determine the range of kinetic energy

Now that we have calculated the athlete's kinetic energy, we can find which range it falls under. The choices are: (A) 200 J - 500 J (B) 2 脳 10^5 J - 3 脳 10^5 J (C) 20,000 J - 50,000 J (D) 2,000 J - 5,000 J Since 3500 J falls into the range of option (D) (2000 J - 5000 J), the correct answer is: (D) 2,000 J - 5,000 J

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