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:
$\begin{aligned} & \text{A}\text{. 200J - 500J} \\\ & \text{B}\text{. 2}\times \text{1}{{\text{0}}^{5}}\text{J - 3}\times \text{1}{{\text{0}}^{5}}\text{J} \\\ & \text{C}\text{. 20000J - 50000 J} \\\ & \text{D}\text{. 2000J - 5000J} \\\ \end{aligned}$

Answer 1

First look at the question to find the values that are given. Now, calculate the speed or the velocity from the given values. Now estimate the average range of mass or weight of an athlete. So, after that write the formula for kinetic energy and solve it for the upper range and the lower range to find the correct answer.

Formula used: $speed=\dfrac{\text{distance}}{time}$
$k=\dfrac{1}{2}m{{v}^{2}}$

Complete step by step answer:
At first we have to look at the question carefully to look for the values given in it,
We see that the distance covered by the athlete(s) = 100m
And the time taken to cover this distance is 10s.
So we know that the speed of an object is $speed=\dfrac{\text{distance}}{time}$
Now, we know both the values, so
$speed=\dfrac{100}{10}m/s$,
Which will give us speed = 10 m/s.
Now, we know the formula for kinetic energy is $k=\dfrac{1}{2}m{{v}^{2}}$.
We know or we must estimate that the average weight of a man may vary from 40kg to 100kg.
So, the range of kinetic energy must be,
$k=\dfrac{1}{2}\times 40\times {{10}^{2}}J$and $k=\dfrac{1}{2}\times 100\times {{10}^{2}}$,
Which on calculating gives us,
2000J and 5000J respectively,

So, the correct answer is “Option D”.

Note: In the formula $k=\dfrac{1}{2}m{{v}^{2}}$, ‘m’ is the mass of the body and ‘v’ is the velocity or speed of a body. The students must keep a knowledge of the average range of weight of an athlete to solve the question.