Animated Solution for Physics - Work, Energy, and Power: An athlete in the olympic games covers a distance of $100$ m in $10$ s. His kinetic energy can be estimated to be in the range

An athlete sprinting down a track is a beautiful display of biomechanics and physics in action. But how do we quantify the energy of such a dynamic event when we aren't given all the variables? This problem is a brilliant exercise in estimation—a crucial skill for any physicist.

We are told that an Olympic athlete covers a distance of $100$ m in $10$ s. We need to find the range of his kinetic energy. The formula for kinetic energy is:

To use this formula, we need two quantities: the mass ($m$) of the athlete and his velocity ($v$). We can easily find the average velocity using the given distance and time:

Here is where the problem tests your real-world intuition. We are not given the mass of the athlete. However, we know that an average adult human, especially a sprinter, typically weighs somewhere between $60$ kg and $80$ kg. Let's assume a reasonable average mass of $m\approx 65$ kg.

Now, we substitute our estimated mass and calculated velocity into the kinetic energy equation:

Our estimated kinetic energy is $3250$ Joules. Now, let's look at the given options. The value $3250$ J falls perfectly within the range of $2000$ J to $5000$ J.

Even if we had assumed a slightly different mass, say $80$ kg, the kinetic energy would be $\frac{1}{2}\times 80\times 100=4000$ J, which still comfortably sits in the same range. This shows the robustness of our estimation. Therefore, the correct option is (d).