Question

An athlete in the Olympic Games covers a distance of 100m in 10s. His kinetic energy can be estimated to be in the range:
A. 20,000 J – 50,000 J
B. 2,000 J – 5,000 J
C. 200 J – 500 J
D. $2\times {10}^5\text{J}-3\times {10}^5\text{J}$

Answer 1

Hint: We are given the distance covered and time taken to cover the distance by an athlete. And we are asked to find the estimated kinetic energy of the athlete. To find kinetic energy we require mass and velocity of the body. Velocity can be obtained from distance and time. Since mass of the body is not given, we can assume the mass of an athlete. Thus we can solve the problem.

Formula used:
Average velocity of the body,
$\begin{array}{rl}& v\text{=}{\displaystyle \frac{\text{distance}}{\text{time}}}\\ & v={\displaystyle \frac{s}{t}}\end{array}$
Kinetic energy of the body,
$KE={\displaystyle \frac{1}{2}}m{v}^2$

Complete step by step answer:
In the question we are given the time and distance covered by an athlete in the Olympic Games.
Distance covered = 100m
Time taken to cover the distance = 10 s
We need to find the kinetic energy of the athlete.
We know that, kinetic energy is given by the equation,
$KE={\displaystyle \frac{1}{2}}m{v}^2$ , were ‘KE’ is the kinetic energy, ‘v’ is the average velocity, and ‘m’ is the mass.
We are given the total distance and total time taken, hence the average velocity,
$\begin{array}{rl}& v\text{=}{\displaystyle \frac{\text{distance}}{\text{time}}}\\ & v={\displaystyle \frac{100}{10}}\\ & v=10m/s\end{array}$
We are not given the mass of the athlete.
Hence in this case we can assume the mass.
We know that the mass of an athlete can vary between 50kg – 65kg.
Therefore the average mass of an athlete can be assumed as 60kg.
Now we can calculate the kinetic energy,
$\begin{array}{rl}& KE={\displaystyle \frac{1}{2}}\times 60\times {10}^2\\ & KE=3000J\end{array}$
Therefore, the estimated range of kinetic energy of an athlete is 2000 J – 5000 J.
Hence the correct answer is option C.

Note:
Since we assume the mass here, the answer can vary according to the assumption, to a limit. But we can be sure that the mass of an athlete will never be less than 40 kg.
Even if we consider 40 kg as the average mass, we get kinetic energy,
$\begin{array}{rl}& KE={\displaystyle \frac{1}{2}}\times 40\times {10}^2\\ & KE=2000J\end{array}$
In this case also the estimated kinetic energy lies in the region, 2000 J – 5000 J.